Second derivative Definition and 174 Threads

Homework Statement \begin{pmatrix} -2 & 0 & 0\\ 0 & -2 & 0\\ 0 & 0 & -2 \end{pmatrix} If I evaluate with eigenvalues, I get: det\begin{pmatrix} -2-\lambda & 0 & 0\\ 0 & -2-\lambda & 0\\ 0 & 0 & -2-\lambda \end{pmatrix}=0 (-2-\lambda{)}((-2-\lambda{)}(-2-\lambda{)})=0 and thus...

Homework Statement Find the second derivative of e^t + t^e : Homework Equations (e^u) = u' * (e^u) The Attempt at a Solution e^t + t^e 1* (e^t) + e*[t^(e-1)] ^^^first derivative (e^t) + e*e[t^{(e-1)-1}] ^^^ 2nd derivative Answer?: (e^t) + e^2[t^(e-2)]

Homework Statement http://imageshack.us/photo/my-images/717/unleddym.png/ Homework Equations The Attempt at a Solution I was wondering why the second derivative at t=1 does not exist but exists at the first derivative. What I did was draw the graph of the function, then the...

Homework Statement If xy + 9e^y = 9e, find the value of y'' at the point where x = 0. Homework Equations product rule The Attempt at a Solution Okay so first I found the first derivative using implicit differentiation and I got: [SIZE="5"]y'=\frac{-y}{x+9e^{y}} then, I found the...

Homework Statement Let y = s(t) represent the number of students who have contracted measles at time t (days). Give an interpretation for each condition: e) s' = 0, s" > 0 The Attempt at a Solution This seems counterintuitive to me, to think that the second derivative is also not...

Homework Statement Find the second derivative of x^3+y^3=1 by implicit differentiation. The Attempt at a Solution I found the first derivative to be x^2/y^2. Do I then use the first derivative and take the derivative of that? I tried to do this, but got stuck on what to do.

Hello! I am wondering if someone could let me know if my understanding is right or wrong. The Taylor series gives the function in the form of a sum of an infinite series. From this an approximation of the change in the function can be derived: f_{a} and f_{a,a} are the first and second...

urgent! second derivative test for functions of 2 variables Homework Statement f(x,y)=x^4 - y^2 - 2x^2 + 2y - 7 Homework Equations classify points (0,1) and (-1,1) as local maximum, local minimum or inclusive The Attempt at a Solution f(x,0)=4x^3 - 0 - 4x + 0 - 0 = 4x^3-4x...

Homework Statement x^6 + y^6 = -6 I have to prove that y'' = 30x^4/y^11 Homework Equations The Attempt at a Solution Using implicit differentiation: 6x^5 + 6y^5 dy/dx = 0 6y^5 dy/dx = -6x^5 dy/dx = -x^5/y^5 Quotient Rule: [(y^5)(-5x^4) - (-x^5)(5y^4 dy/dx)] /...

Homework Statement Find the second derivative of 4x^2 + 3x - 9y^2. Answer in terms of y. Homework Equations All derivative formulas. The Attempt at a Solution [PLAIN]http://http://i52.tinypic.com/2w2ptex.jpg I can't get much further than this; the thing that gets me is how to put...

Hi everybody. I have a question regarding an example problem at about 22min on this lecture http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-2-eulers-numerical-method-for-y-f-x-y/ The equation in question is y'=x^{2}-y^{2}. In an...

Second Derivative Homework Statement f(x) = sin (2x)^1/2 find the f"(x). Homework Equations The Attempt at a Solution I don't know homework to do it...

[b]1. Homework Statement [/ Using the approximation, explain why the second derivative test works approximation=f(x0+delta x, y0+delta y) delta x and delta y are small... Homework Equations f(x0+delta x,y0+delta y) The Attempt at a Solution ok so i know the first derivative...

Homework Statement I am doing the various ins and outs of curve sketching and the mean value theorem and all that jazz with this function: f(x)=sec(x)+tan(x) Homework Equations The Attempt at a Solution I took the first derivative to be: f'(x)=sec(x)tan(x)+sec^{2}(x) I am having...

Homework Statement Knowing that: \frac{dz}{dx}=\sqrt{\frac{(-T)^2}{(k*(z-a)*(z-2*b+a)/2-T*cos(phi))^2}-1} What is: \frac{d^2z}{dx^2} ? Homework Equations I'm trying to solve using this general equation I found on Wikipedia...

Alright. So I have dy/dx = -1-y2. I want to take the second derivative to get some information about the concavity of the solution, but I can't wrap my head around what's really going on. What I think I know: I have an ODE that is dependent on the dependent variable, so my solution will only...

Hey there, I have a problem to do, in which I need to determine the acceleration of an object and the uncertainty of the acceleration. The position vs. time equation is given by: s(t) = 0.205t2 + 0.3001t Therefore, after differentiation, I can state the the velocity vs. time equation...

Hi, I am having a little trouble understanding something my lecturer said about using the table of signs to check whether there exists a point of inflection when y'' = 0. I understand that in order for there to be a point of inflection at x0 say, I require to check the value of y'' at either...

Homework Statement r = 2/(2 - cos (\pi*t)) Homework Equations N/A The Attempt at a Solution Hello everyone, first I would just like to say (which is obvious since I'm asking :-p ) That it's been a long long time since I've had to do derivatives, hence my total cluelessness with...

Homework Statement if d/dx(f(x)) = g(x) and d/dx(g(x)) = f(x^2), then d^2/dx^2 ( f(x^3) ) = ? Homework Equations The Attempt at a Solution from 1 and 2 we get d.dx(g(x)) = d2/dx2(f(x)) = f(x^2) but then what? That doesn't tell me anything about f(x^3) Please help.

Homework Statement Use Maclaurin's theorem to estimate d^{2}y/dx^{2} at x=0 It's the deflection of a 2m beam, where x is the distance along the beam, y is the deflection in mm. Homework Equations The Attempt at a Solution I didn't know where to start so I tried to solve it a different...

Second derivative... Homework Statement Okay, this is a rough one for me. It was a question I got on my test, and (obviouslly) didnt get right. I am studying all my old exams for my final in 2 days and this is the last of the problems that I can't wrap my head around...any help would be...

I have this problem for homework dealing with second derivatives and graphs. I have no problem finding derivatives usually, but this one is giving me trouble. I cannot figure out how to get the second derivative. I have an idea of what to do, but need some extra guidance. Find f '(x) where...

Homework Statement Find the second derivative (y") of y=xtanx. The attempt at a solution I got the first derivative (y') y=xtanx y'=x(secx)+tanx I started the second derivative and got stuck y"=xsec^2x+tanx

Hello, I am facing a diffusion equation.. \frac{du(x,t)}{dt} = D \frac{d^2u}{dx^2} .. with slightly exotic boundary conditions: u(0,t) = 0 \frac{d^2u(a,t)}{dx^2}+ \alpha \frac{du(a,t)}{dx} = 0 I expected the solution to be relatively easy to find, since separation of variables quickly...

Homework Statement x = t - e^{t} y = t + e^{-t} Find dy/dx and d^{2}y/dx.Homework Equations Derivative equations.The Attempt at a Solution dy/dt = 1 - e^{-t} dx/dt = 1 - e^{t} The dy/dx I came up with is: dy/dx = (1 - e^{-t}) / (1 - e^{t}) Second derivative I came up with is: d^{2}y/dx = -...

Homework Statement I trying to find the second derivative of xe^x Homework Equations chain rule The Attempt at a Solution Two find the first derivative I use the chain rule. f'(y)g(y)+f(y)g'(y) so I get e^x+xe^x is the second derivative e^x+f'(y)g(y)+f(y)g'(y)...

f(x)= 1/125(e5x)(5x-2)I think this is the first derivative but I ain't good at math and gives me some headaches I used the product rule.. but still I have doubts =( f '(x)= 1/125(5)(e5x)(5x-2) + (5)(1/125(e5x) Please help me! :cry: I need to understand how to do this

Hello-- I'm in the process of implementing a PML for FDTD modeling. I would like to take the derivative of the partial derivative shown below, but I am uncertain with respect to how I might proceed. \[ \frac{\partial }{{\partial x}} \to \frac{1}{{1 + \frac{{i\sigma \left( x \right)}}{\omega...

Can someone tell me what this actually is. So, in the case when the Hessian is positive (or negative) semidefinite, the second derivative test is inconclusive. However, I think I've read that even in the case where the Hessian is positive semidefinite at a stationary point x, we can still...

Homework Statement For example with f(x,y) = x2y + xy2 Homework Equations The Attempt at a Solution Well I know there is a critical point at (0,0). So I calculated the second derivatives but they are all 0 here so that doesn't help. I also tried using the Taylor expansion to...

Homework Statement Find y''(x) of the parametric equation 9x^2+y^2=9 using implicit differentiation. Homework Equations I already came up with y'(x) = -9x/y The Attempt at a Solution Here is what I have for y''(x) so far y''(x) = d/dx (-9xy^-1) =-9(d/dx)(xy^-1)...

Homework Statement Find the second derivative of: e^{ax} and e^{-ax} Homework Equations The Attempt at a Solution The book that I am using seems to have been very vague on how to take the derivatives of exponential functions. I am aware that: \frac {d(e^{x})}...

clear all; nx=50; ny=30; hx=pi/nx; x=linspace(0,pi,nx+1); y=linspace(0,pi,ny+1); x_plus_h=x+hx.*ones(1,nx+1); x_minus_h=x-hx.*ones(1,nx+1); for i=1:nx+1 for j=1:ny+1 f_xx(j,i)=(f9(x_plus_h(i),y(j))-2*f9+f9(x_minus_h(i),y(j)))./(hx.^2); end; end; [xx,yy]=meshgrid(x,y)...

Homework Statement f(x)= x^(3)e^(x) Find f'(x) in simplest form. Find f"(x) in simplest form. Homework Equations The Attempt at a Solution I found the first derivative to be: (using the product rule) f'(x) = (e^x)[3x^2] + (x^3)[e^x] f'(x) = 3x^(2)e^(x) + x^(3)e^(x) f'(x) = x^[2]e^[x](3 + x)...

Homework Statement Find the exact value of f''(2) if f(x)=\sqrt{3x-4} Homework Equations See above The Attempt at a Solution I've tried to use the product rule to differentiate. f= x(3x -4)^{\frac{1}{2}} f'= (3x -4)^{\frac{1}{2}} + \frac{3}{2}^{\frac{-1}{2}} f''=...

Homework Statement The function Sh(t) = 30[cos(16.04*)]t models the horizantal position of a pellet with respect to time. Find the first & second derivatives of Sh(t). Homework Equations The Attempt at a Solution I attached a word document because I lack the ability to put...

Homework Statement A curve has equation y=e^2x-x^2+x-3 , find value of x for which d^2y/dx^2=0. Homework Equations The Attempt at a Solution well. i started by finding out the 1st and 2nd derivative: y=e^2x-x^2+x-3 dy/dx= 2e2^x-2x+1 and d2y/dx2=4e^2x-2 = 0 dy/dx =>2e^2x=2x-1...

Homework Statement Assuming sufficient differentiability, find second derivative of F(x) = integ[a,x] (t-x)2 f(t) d(t) Homework Equations Probably Fund.Thm of Calculus and some properties The Attempt at a Solution I really have no idea..I tried evaluating but with t=x but I get...

Homework Statement Suppose f(3)=2 , f'(3)=5 , and f''(3)= -2 . Then d²/dx² (f²(x)) at x=3 is equal to ____? A. -20 B. 20 C. 38 D. 42 E. 10 The Attempt at a Solution I am confused about how to find the function to get the derivative from that function. Any Ideas? Thanks.

If x and y are defined in terms of a third vatiable say t , then to find d2y/dx2 , we cannot find d2y/dt2 and d2x/dt2 and divide them to get d2y/dx2 , i am unable to fingure out the reason for this !

Does the second derivative test fail for x3 at x=0: f'(x)=3x2 f''(x)=6x , for x=0, f'(0)=0 & f''(0)=+ve , so it should be a point of local maxima , but it is not!

How would you find the second derivative of an implicit function? y^2-x^2=16 Heres my attempt: 2y(dy/dx)-2x=0 2y(dy/dx)=2x 2y(dy/dx)/2y=2x/2y dy/dx= x/y This is only the first derivative. I think I'm suppose to plug in dy/dx back into the original equation. Am I on the right track?

I often see the second derivative written down like this: \frac{d^2y}{dx^2} Although it seems more logical to me to write \frac{d^2y}{d^2x^2} Or \frac{d^2y}{(dx)^2} Since it represents \frac{d}{dx} \frac{dy}{dx} Is there any logic behind this or is it just a shortcut notation to omit...

Let f(x)=x^2/(1-x^2 ) a) Find f'(x) b) Find f"(x) For the answer to a) they give f'(x)=2x/〖(1-x^2)〗^2 and for b) f"(x)=2 (1+〖3x〗^2)/〖(1-x^2)〗^3 Now after many rounds of trying i have not been able to get an answer remotely close to what they have given. i don;t know if it is due to me...

Homework Statement find f''(x) if f(x) = sqrt(x) * e^(-x) and then find the roots of f''(x) // I am trying to do the 2nd derivative test (need f''x) and then find inflection points// Homework Equations my methodology| d/dx sqrt(x) = 1/(2*sqrt(x)) and d/dx e^(-x) = -e^(-x)...

how would I find the first and second derivative of (x^3/3) - 2x^2 + 3x +8 thanks

Let a function v in one variable, say u u is a function also, but in two variables, say x & y for the first derivative of v, i did the following: \frac{\partial v}{\partial x} = \frac{d v}{d u} . \frac{\partial u}{\partial x} And the resutlt is: \frac{\partial v}{\partial x} = cos(u) . u_x...

Homework Statement Find the second derivative of 3sec\sqrt{x} Homework Equations derivative of sec u = secu(tanu)*u' product rule- (F*G)'=f'*g+g'*f quotient rule- (F/G)'=(f'*g-f*g')/g^2 The Attempt at a Solution So i did the first derivative of it, getting...

Determine the value of r in terms of l, k, and m for which the following function has a minimum. V(r) = -(k/r) + (l^2/(2mr^2)) where l, k, and m are positive constants. Prove that this is a minimum by showing that the second derivative of V(r) at the minimum is positive. I have no...