Question

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Answer 1

Looking at each of the answers:

I. The graph of f has a critical point at x = 0.
A critical point exists when f'(x)=0 and the graph shows that f'(0)=0 as required. True.

II. The graph of f has a critical point at x = 1.
f'(1)=-1 so this is false.

III. The graph of f has a point of inflection at x = 1.
The f'(x) goes from negative to positive gradient at the point x=1 so this is true.

Answer 2

thank you so much!!