Question

Given the graph of f Œ(x), the derivative of f(x), which of the following statements are true about the graph of f(x)?
I. The graph of f does not have a point of inflection.
II. The graph of f has a point of inflection at x = 2.
III. The graph of f has a critical point at x = 2.

Answer 1

@AnswerMyQuestions @ganeshie8 @iGreen @JFraser

Answer 2

@DanJS

Answer 3

@PRAETORIAN.10

Answer 4

You can ask this in the math section. I am sure you will get much more help there. :)

Answer 5

the graph shows the derivative of f(x).
what does the first derivative of a function tell us, in general?

1. expect a min/max (i.e. critical point) where f'(x)=0 in the graph this happens at x=0 and x=4

2. what else do we know about f'(x)? It tells us the slope of the original function. Here f'(x) is positive from x=0 to x=4 so the original function is rising.

3. the second derivative =0 tells where we may have an inflection point. Here in this graph, the slope of f'(x) is the second derivative, and at x=2 (at the "peak") the slope is 0. That is, we have an inflection point where the original curve changes from "concave down" to "concave up"