Second derivative Definition and 174 Threads

Homework Statement find f''(x) <-- second derivative f(x) = 3e^-x2 <-- that 2 is x squared Homework Equations The Attempt at a Solution my attempt was 6x^2 e^x2

I'm having trouble seeing how an example comes out because the "worked example" skips about 5 steps and I can't get from point a to b. It starts as: \frac{\frac{d}{dt}(\frac{3t^{2}-3}{3t^{2}-6t})}{3t^2-6t} and is meant to end up as: \frac{-2(t^{2}-t+1)}{3t^{3}(t-2)^{3}} I end up with a...

Homework Statement yet is approaching negative infiniti? We were discussing a question that went "suppose f double prime (x)>0 and x ranges from negative infiniti to infiniti, and f(a)=0. Prove or disprove that f(x) is bounded below." The man said that e^-x - x had a second derivative...

It is a standard fact that at any point p in a Riemannian space one can find coordinates such that \left.g_{\mu\nu}\right|_p = \eta_{\mu\nu} and \left.\partial_\lambda g_{\mu\nu}\right|_p. Consider the Taylor expansion of g_{\mu\nu} about p in these coordinates: g_{\mu\nu} = \eta_{\mu\nu}...

Homework Statement Show that y(t) = e^t is a solution of y'' - y = 0, Homework Equations integral of e^x dx = e^x +c derivative of e^x = e^x The Attempt at a Solution set m = d(e^t)/dt, which also = e^t then dm = e^t then d(m)/dt = e^t if y(t) = e^t is a solution integrate...

Homework Statement Given y=xtanx, find y'' (second derivative) Homework Equations Uh... I'm not even sure if I'm using the right one... d/dx(tanx) = sec^2x The Attempt at a Solution y=xtanx y'= (x)(sec^2(x)) + (tanx)(1) y'= xsec^2(x) + tanx y'' = [(x)(2sec^3(x)) +...

Homework Statement Given (d^2)x/ (dt^2) = 2 for all t>= 0 and dx/dt= -5 and x= 4 when t= 0 find t when a) dx/ dy= 0 b) x= 0 2. The attempt at a solution a) Given (d^2)x/ (dt^2) = 2, then dx/dt= 2x + c = -5 given dx/ dt= 0 then 2x + c= 0 c= -2.5 using 2x + c= 0 and 2x + c =...

[SOLVED] easy second derivative question Homework Statement "If y^2 - 3x =7 what is the second derivative?" Homework Equations Answer choices: A) -6/7y^3 B) -3/y^3 C) 3 D) 3/2y E) -9/4y^3 The Attempt at a Solution I got the first derivative to be: 3/2y Second derivative...

Hello I am trying to figure out the second derivative of \frac{\partial^2 z}{\partial x^2} and \frac{\partial^2 z}{\partial t^2} z(u) and u=x-vt i found the first derivate of \frac{\partial z}{\partial x} to be \frac{\partial z}{\partial x}= \frac{\partial z}{\partial u} *...

Homework Statement Find all relative extrema using the second derivative test for H(x) = x * lnx Homework Equations The Attempt at a Solution H'(x) = (1 * ln x) + (x * 1/x) = lnx + 1 H''(x) = 1/x + 0 Is H''(x) right? Then I am having trouble finding the relative extrema from...

Just wondering how you take the second derivative when using the quotient rule. After using the quotient rule to get my first derivative, I tried again and the numerator ended up as 0.

I would like someone to tell me what is the geometric interpretation of the second derivative at a fixed point, or in an interval?? thx

Homework Statement Show that lim(h-->0) [f(x+h)-2f(x) + f(x-h)]/h^2 is equal to f''(x) for any given value of x where the second derivative exists. I'm supposed to use L'Hopitals rule for this problem. I did and got [f(x+h)-f(x-h)]/2h Now I am stuck. I thought about adding and...

I was wondering if someone could show me where to go next in this problem. I need to determine the minimum length, width and height that a 1 cubic foot box can have. This box does not have a top. I know that I need to minimize the area, but I'm not sure if I'm going about this correctly. So...

Were assigned questions regarding implicit differentiation and the second derivative but did not receive a formal lesson so I need some explanations. Example: Find the second derivative x^3 + y^3 = 1 I found this solution on the internet and the answer matches the one in the textbook...

I am Calculus AB student. I know how to find first derivative, second derivative, prove points of inflecition, find concavity...but as I just finnished the last section of chapter 4 and chapter 5 is Integrals, I still have one question that remains unanswered: Why is it important to find...

I am posting my theorems for peer review, anyone interested in posting some proofs using some simple functions? Can these theorems be reduced into simpler equations? Orion1 Second Derivative Theorems: \frac{d^2}{dx^2} (x) = 0 \frac{d^2}{dx^2} (x^2) = 2 \frac{d^n}{dx^n} (x^n) = n...

Starting with y^2-xy=2, then y'=y/(2y-x) y''=(2y-x)y'-y(2y'-1)/(2y-x)^2 substitute y' in: y''=(2y-x)(y/2y-x) - y(2(y/2y-x)-1) the (2y-x) cancels: y''=(y) - y(2y/2y-x)-1) distribute: y'' = y - (2y^2)/(2y-x)-y Somewhere I need y^2-xy so I can replace it with the original 2, but...

I've been working on this problem lately where I've been looking at the second derivatives of 2D and 3D density fields. Now, the second derivatives of the field can be represented in a matrix, which can be thought of as an N-dimensional ellipse with the principal axes aligned along some angle...

I have a problem on finding the second derivative for this function: \frac {x}{x^2-4} For the first derivative, I got: \frac {-x^2-4}{(x^2-4)^2} Now here is where I am stuck! So far for the second derivative, I got this (Please check!): \frac...

I have a problem on finding the second derivative for this function: \frac {x}{x^2-4} For the first derivative, I got: \frac {-x^2-4}{(x^2-4)^2} Now here is where I am stuck! So far for the second derivative, I got this (Please check!): \frac...

Find the second derivative by implicit differentiation: x^3 + y^3 = 6xy Wow, a lengthy question when you have to show all your work. Anyway, for the first derivative I got: \frac {2y-x^2}{y^2-2x} How would one start to calculate the second derivative? I tried the Quotient Rule...

Hello, this is my first post in this site, so here goes: Im working on a Matlab program. I have to calculate the second derivative of a given equation. The problem is that plotting the derivative is necessary, and that's where I'm stuck. Here's what I've got so far: % Evaluar f(x) y...

Any help you can give me would be appreciated! The teacher wrote the solution to the problem on the board without giving much explanation of how he got there, and now he wants the third derivative, so I was wondering if you could help answer how he got the second. g(x) [the lim. as x goes...