Question

The graph of f ′(x) is continuous and increasing with an x-intercept at x = 0. Which of the following statements is false?

Answer 1

@rational

Answer 2

If \(f'(x)\) is increasing, that means \(f''(x)>0\). What does this say about concavity?

If \(f'(x)=0\) for \(x=0\), this means \(x=0\) is a critical point of \(f(x)\), so an extremum occurs for \(f(x)\).

Inflection points are points for which \(f''(x)=0\). Are you given any info about this?

Answer 3

this is all info given

Answer 4

I'm aware, I'm specifically asking you if you see any info given about the x-intercepts of the second derivative.

Answer 5

My post above is intended as a set of hints for eliminating some of the wrong answer choices.

Answer 6

idk @SithsAndGiggles