# Derivative homework

1. Feb 8, 2010

### Nope

1. The problem statement, all variables and given/known data
Can someone check my homework?
http://img10.imageshack.us/img10/9686/48742895.jpg [Broken]
http://img229.imageshack.us/img229/6981/52780988.jpg [Broken]
http://img297.imageshack.us/img297/6955/85086758.jpg [Broken]
http://img11.imageshack.us/img11/1221/86324492.jpg [Broken]
thx!

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. Feb 8, 2010

### Staff: Mentor

Re: Derivative

In problem 2 you have a mistake.
You have
C = 2sqrt(A*pi) = 2(A*pi)^(1/2) = (A*pi)^(-1/2) *pi

The 2nd and 3rd expressions above are not equal. You have apparently taken the derivative, but you show it as being equal to C. The derivative of C is not equal to C.

3. Feb 8, 2010

### Nope

Re: Derivative

Oh, I forgot to put C'!
Is that the only mistake i got?

4. Feb 8, 2010

### Staff: Mentor

Re: Derivative

You got the right answer, but make sure you understand the difference between C'(A) and C'(81)

C'(A) = sqrt(pi/A)
C'(81) = sqrt(pi/81) $\approx$ .1969

Another way to write what you're doing is this:

$$\frac{\Delta C}{\Delta A} \approx \frac{dC}{dA}$$
$$\Rightarrow \Delta C \approx \frac{dC}{dA} \Delta A$$
$$\Rightarrow \Delta C \approx \frac{dC}{dA}|_{A = 81} \Delta A$$
$$\approx .1969 * 1 = .1969$$

Everything looks fine for the other problem.