How do you find all values of s that satisfy the Mean Value Theorem for f(s)=(4s+16)^(2/3) on the interval [-7,-4] without a calculator?

Question

anonymous · Answer

Mean Value Theorem guarantees a value of c on [-7,-4] such that f'(c) = [f(-4)-f(-7)]/(-4 - (-7)]

So you need the derivative of the function.

anonymous · Answer

I did that, but its determining the correct way to solve it that I have trouble with. I found the derivative as $$\frac{ 8 }{ 3\sqrt[3]{4s+16} }$$ and set it equal to the average slope, $$\frac{ -12^{2/3} }{ -3 }$$, but I don't know what do after that.

myininaya · Answer

Hey. I don't like my s being on bottom. Maybe you might want to multiply both sides by that cube root part or even multiply both sides by 3 time that cube root part.

myininaya · Answer

Or if the thing that makes you mad is the cube root, then cube both sides to get rid of the cube root.

myininaya · Answer

I would end up doing the combination of the two things. :)