Question

Given the graph of f '(x), the derivative of f(x), which of the following statements are true about the graph of f(x)? (4 points)

2.
Given the graph of f '(x), the derivative of f(x), which of the following statements are true about the graph of f(x)?

Graph is parabola with x intercepts at x equals 0 and 3 and vertex at x = 1

I.The graph of f is decreasing on the interval (0, 2).
II. The graph of f is increasing on the interval (1, infinity).
III. The graph of f has point of inflection at x = 0.


a I only
b II only
c III only
d None of these are true

Answer 1

(I) is true, since the plot shows f'(x) is negative on (0, 2)

(II) is false, since f'(x) is negative on (1, 2), so f(x) is decreasing over this interval

(III) is false. An inflection point can only occur at a point x if f''(x) is zero or doesn't exist. But at x = 0, the tangent line to f'(x) clearly has a negative, non-zero slope.

This makes A the correct choice.