Use WolframAlpha to accomplish the following:

Let \( f(x) = \frac{1}{5} x^5 + x^4 -4 x^3 + 3 \) on \( [-8, 4] \).

- Find the "critical numbers" of \( f(x) \).
- Plot \( f'(x) \). What happens to the derivative at the critical numbers?
- Find the extrema of \( f(x) \) with their locations.
- How do the locations of the extrema compare to the critical numbers?
- Notice an unusual result when \( x=0 \).
- Notice an unusual result when \( x=-6 \).