Question

I'm doing test corrections, and it's been a few weeks since we did this, so I'm a little fuzzy. I'm supposed to find the zeros, relative extrema, and inflection points of f(x) = x^3 - 6x^2 + 3x + 10.

The zeros would be -1, 2, and 5 right?

Then I would take the derivative of that and get that f'(x)=3x^2-12x+3.

Then what do I do from here? I vaguely remember something about finding critical points using intervals, but I don't really remember how to do that. Do I maybe need the second derivative?

Answer 1

f has a max/min where f'=0 and f''≠0
f is increasing where f' > 0
f is concave up where f'' > 0
f has an inflection point where f'' = 0