Question

Consider the function f(x) = 3/4x^4 –x^3 -3x^2 + 6x , find the relative extrema for f(x), be sure to label each as a maximum or minimum.

How do I find the x-values of what it is asking?

Answer 1

better review your max/min topic. f has a max/min where f'=0 and f"≠0.

f' = x^3-3x^2-6x+6

This does not factor over the rationals, so a graphical solution is probably the best bet. The graph of f' is at

http://www.wolframalpha.com/input/?i=x^3-3x^2-6x%2B6

So, where f'=0, f will have a max or min. Just using what you know about the shape of quartics, you should be able to decide which are the maxes and which are the mins, without checking f".