Derivative Homework: Checking Answers with Step-by-Step Solutions

[Nope]

Homework Statement

Can someone check my homework?
http://img10.imageshack.us/img10/9686/48742895.jpg
http://img229.imageshack.us/img229/6981/52780988.jpg
http://img297.imageshack.us/img297/6955/85086758.jpg
http://img11.imageshack.us/img11/1221/86324492.jpg
thx!

Homework Equations

The Attempt at a Solution

 

[Mark44]

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.

 

[Nope]

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.

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

 

[Mark44]

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.