1. ### Application of derivatives

Homework Statement the original function is ##−6 x^3−3x−2 cosx## ##f′(x)=−2x^2−3+2sin(x)## ##−2x^2 ≤ 0## for all x and ##−3+2 sin(x) ≤ −3+2 = −1##, for all x ⇒ f′(x) ≤ −1 < 0 for all x The Attempt at a Solution this problem is part of a larger problem which says there is a cubic...
2. ### Find stationary points of a two variable function involving

Homework Statement Find all stationary points of the function G(x, y) = (x^3)*e^(−x^2−y^2) Homework Equations fx=0 and fy=0 The Attempt at a Solution Gx = 3x^2*e^(-x^2-y^2) +x^3(-2x)e^(-x^2-y^2) = e^(-x^2-y^2)(3x^2-2x^4) Gx = 0 implies 3x^2-2x^4=0 x^2(3-2x^2)=0 hence x =0 ,+or-...
3. ### Question about the derivation of the energy momentum tensor

Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf Homework Statement As it says in the pdf: "Based on Noether's theorem construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. L=-1/4...
4. ### What is the Higher Derivative of a function?

I'm relatively new to calculus and I have a new chapter in my study which is on the Implicit Function, Implicit Differentiation and Higher Derivatives of a function, the problem is I don't understand the meaning of a 2nd or 3rd or whatever the higher derivative of a function is, what I know is...
5. ### Splitting a Derivative

After doing a couple courses in physics as well as calculus and differential equations, I was starting to wonder about splitting a derivate, such as ## \frac{dy}{dx} ##, into seperate pieces ##dy## and ##dx##. I know we've never done it in calculus or differential equations because it isn't...
6. ### Distance formula maximization problem

Homework Statement At 9 P.M. an oil tanker traveling west in the ocean at 18 kilometers per hour passes the same spot as a luxury liner that arrived at the same spot at 8 P.M. while traveling north at 23 kilometers per hour. If the "spot" is represented by the origin, find the location of the...
7. ### I'm curious what anyone gets for part d

Homework Statement After a wild ride on a windsurfer, you head to a lifeguard tower to fly a kite. You stand on the tower, which is 3 meters above the ground and release your kite. You let out 10 meters of string and the kite begins moving according to the following equation: y(t) = (0.9...
8. ### Why is the first derivative velocity?

Just something that has been bugging me. Can someone bestow why the first derivative is velocity and the second derivative is acceleration. I want to conceptually understand this. Thank you
9. ### Calc BC derivative problem with trig and double angle -- Help please

Homework Statement Find f'(x) if f(x) = 8^(sin^2(3x)) Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it. Homework Equations if y=a^u then y' = ln a * a^u * du sin(2x) = 2sinxcosx The Attempt at a Solution We're...
10. ### How to find the equation of this tangent?

Mod note: Thread moved from Precalc section Homework Statement F(x)=sqrt(-2x^2 +2x+4) 1.discuss variation of f and draw (c) 2.find the equation of tangent line to (c) that passes through point A(-2,0) The Attempt at a Solution I solved first part I found the domain of definition and f'(x)...
11. ### Finding the distance from origin to a tangent line

Homework Statement Find the distance between the origin and the line tangent to ##x^\frac{2}{3}+y^{\frac{2}{3}}=a^{\frac{2}{3}}## at the point P(x,y) Homework Equations [/B] Distance= ##\frac{\left |a_{0}+b_{0}+c \right |}{\sqrt{a^{2}+b^{2}}}## The Attempt at a Solution To begin I find...
12. ### What version of the definition of derivative

If my understanding is correct the definition of a derivative is lim h->0 (f(x+h)-f(x))/h However, I've also seen this used: lim x->c (f(x)-f(x))/(x-c) are these both considered valid definition for the derivative or does the derivative have to tend towards zero? I am a bit confused because I...
13. ### Question on Mean Value Theorem & Intermediate Value Theorem

Homework Statement for ##0<\alpha,\beta<2##, prove that ##\int_0^4f(t)dt=2[\alpha f(\alpha)+\beta f(\beta)]## Homework Equations Mean value theorem: ##f'(c)=\frac{f(b)-f(a)}{b-a}## The Attempt at a Solution I got the answer for the question but I have made an assumption but I don't know if...
14. ### Confused on these two derivative problems

Homework Statement a. k(t) = (sqrt(t+1))/(2t+1) b. y = (3^(x^2+1))(ln(2)) The Attempt at a Solution For the first problem, I know I use the quotient rule for derivatives (L)(DH)-(H)(DL)/((L)^2) which would go to: ((2t+1)(1/(2sqrt(t+1)) - (sqrt(t+1))(2))/((2t+1)^2) I get stuck here, maybe...
15. ### How does the Kalman filter calculate derivatives?

Suppose we have a Kalman filter. We have a position sensor, for example GPS. We use the filter to estimate position. However in all examples I see higher derivatives in the state vector: speed, acceleration and sometimes jerk. There is no sensor that calculates these values directly, so they...
16. ### Velocity Derivative of a Sinusoidal Wave (Counter-Intuitive)

What's the matter: So, I think I have some skills when it comes to differentiation after taking calculus 2 last semester, but when it starts to intertwine with physics, and interpreting physical phenomenon through equations, It appears I could use some help. Anyway, the problem that I got hung...
17. ### Tension on a Rope Deflected by a Pulley: Differentials

Hi all, first post here. I'm a junior Physics/Math double major at UMass Amherst, playing with some problems over the summer. I'll get right into it. A rope with constant tension T is deflected through the angle 2\theta_{0} by a smooth, fixed pulley. What is the force on the pulley? It is...
18. ### 'Wheel-like' Mathematics (Modulating Trig Functions?)

As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation a*(a/b)sin(pi*x) The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can...
19. ### Foundations What's a good book for last year of A levels Maths?

I'm looking for a book to self-study this summer before my last course of Bachillerato (A Levels or High School in other countries). My performance in Mathematics has only improved and I've just been given the maximum mark this last term (10/10 or A+). This has motivated me a lot to keep...
20. ### Derivatives and Linear transformations

Let G be a non-empty open connected set in Rn, f be a differentiable function from G into R, and A be a linear transformation from Rn to R. If f '(a)=A for all a in G, find f and prove your answer. I thought of f as being the same as the linear transformation, i.e. f(x)=A(x). Is this true?
21. ### Deriving formulas used for vectors in physics.

Hey guys and gals, I'm taking an online physics course just to kind of learn the basics before I take the real thing this summer. The course is from OpenYale for those interested (oyc.yale.edu). Anyways, the professor was talking about some formulas for finding ##\vec{r}(t) = r(i(cos\omega t) +...
22. ### Calculus Derivative Terminology

I have attached an image of a function that I fit to a scatter plot, and I would like to know if there is a term for the point on the function at which the slope transitions from being less than -1 to greater than -1. I have highlighted this point approximately in yellow...
23. ### Linear Ordinary Differential Equation: Definition

Homework Statement The website says this: "It is Linear when the variable (and its derivatives) has no exponent or other function put on it. So no y2, y3, √y, sin(y), ln(y) etc, just plain y (or whatever the variable is). More formally a Linear Differential Equation is in the form: dy/dx +...
24. ### Finding y=f(x)

Homework Statement Given two curves y=f(x) passing through (0,1) and ##g(x)=\int\limits_{-\infty}^xf(t)dt## passing through (0,1/n). The tangents drawn to both curves at the points with equal abscissae intersect on the x-axis. Find y=f(x). Homework Equations None The Attempt at a Solution...
25. ### Derivative of metric with respect to metric

I'm hoping someone can clarify for me, I have seen the following used: \frac{\partial}{\partial g^{ab}}\left( g^{cd} \right) = \frac{1}{2} \left( \delta_a^c \delta_b^d + \delta_b^c \delta_a^d\right) I understand the two half terms are used to account for the symmetry of the metric tensor...
26. ### Richardson Extrapolation with 3 steps?

Homework Statement [/B] use richardson extrapolation to estimate the first derivative y=ln(x), x=5 using steps of 2, 1, 0.5. Four decimal points. obtain true relative error for the last estimate and comment on its value. Homework Equations [/B] deriv ln(x)=1/x The Attempt at a Solution I...
27. ### Using the derivative of the formula of the number of nuclei

Hi all, I have a question concerning the derivative of the formula of the number of nuclei. I hope I've posted this in the right section, I'm new here :P. Anyway, in the question, the given values are: At a certain time t, there is an amount of radioactive Br-82. The activity A is 7.4*1014 Bq...
28. ### Maximize volume of a box

Suppose someone gives you a rectangular sheet of length a and width b (so b ≤ a). You make a topless box by cutting out a square with length x out of each corner and folding up the sides. How should you cut the sheet so as to maximize the volume of your box?
29. ### Natural log differentiation question

Homework Statement f(x) = 1/ln (10-x) -- I would assume it to be a fairly simple equation, but I am screwing it up Homework Equations What is f'(x)? The Attempt at a Solution f'(x) = (ln (10-x))^-1 = -(ln (10-x))^-2 * -1 * 1/(10-x) -- 2 negatives cancel out = 1/(10-x)...
30. ### Complex derivative of x: ((x)^(1/x))'

<<Moderator note: Remember that filling in the complete homework template is mandatory in the homework forums. This thread has not been deleted due to containing relevant replies.>> 1. Homework Statement ((x)^(1/x))' Homework Equations This probably isn't overly dificult, but it has got me...