Find the instantaneous rate change of the surface area of a sphere with respect to the radius if the radius is 3cm. (Surface area: S=4pir62) for this do I just plug in 3 for r and that's my answer?

Question

mertsj · Answer

The instantaneous rate of change of Area with respect to radius is the value of the first derivative at the given value of the radius.

anonymous · Answer

What does that mean exactly?

mertsj · Answer

It might help if you would say what you are studying that this question relates to.  It seems to me to be a calculus question.

anonymous · Answer

I'm in honors pre-calc, I'm not really sure how to do this question, as I think we're learning it on monday, but this packet is due monday as well

anonymous · Answer

If I can get some sort of equation, i can apply it, but I don't know what the question really is asking

mertsj · Answer

$$A=4 \pi r^2$$

anonymous · Answer

yes, I have that, can I just plug in 3 for r or is there more to it?

mertsj · Answer

First derivative = 
$$A'=8\pi r$$

anonymous · Answer

Ah, how do you get that?

mertsj · Answer

Multiply by the exponent and reduce the exponent by 1.  It's the first derivative.

anonymous · Answer

and so then to find the instantaneous rate of change I can plug 3 in for r for the equation A' =8(pi)r ?

mertsj · Answer

yes

anonymous · Answer

Alright, simple enough, thanks a lot for your help!

mertsj · Answer

yw