The function V=s^3 describes the volume of a cube, V, in cubic inches, whose length, width, and height each measures s inches. Find the instantaneous rate of change of the volume with respect to s when s = 3 inches.

Question

anonymous · Answer

So I'm assuming I find the derivative of V=s^3 and then plug 3 in for s? Which would give me 27. correct?

whpalmer4 · Answer

Yes, that is correct.  Find the derivative of $V(s)$ with respect to $s$ and evaluate it at $s=3$. 

You can check your answer to see if it is in the right ballpark by evaluating $V(3)$ and $V(3+0.001)$.  What is the slope of the line between $(3,V(3))$ and $(3+0.001,V(3+0.001))$?  It should be very close to your answer.  You are approximating the tangent line to the function at $s=3$ by using a straight line that passes through $3,V(3))$ and has the slope of the derivative of $V(3)$.  Try the experiment with various values for the second point and see how it behaves as you get closer and closer.