# Introduction to extrema

Use WolframAlpha to accomplish the following:

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

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