Exercise 9

Let $f(x) = \frac{1}{4}x^3 + 4$.

1. Sketch a graph of $y = f(x)$ and explain why $f$ is an invertible function.

2. Let $g$ be the inverse of $f$ and determine a formula for $g$.

3. Compute $f'(x)$, $g'(x)$, $f'(2)$, and $g'(6)$. What is the special relationship between $f'(2)$ and $g'(6)$? Why?