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 an inverted parabola with x intercepts at x equals 0 and 4 and vertex at x equals 2.

the graph of f does not have a point of inflection.

the graph of f has a point of inflection at x = 2.

the graph of f has a critical point at x = 2.

i only

ii only

iii only

i and iii only

has a horizontal tangent line at , and it's clear from the plot that is increasing to the left and descreasing to the right. This means when , so there is an inflection point there and only statement II is true.

Statement III is not true because critical points only occur where or (possibly) when is undefined. Clearly when .

they can both be solutions depends on the equation

step-by-step explanation:

what is the equation? ?