Given the graph of f ′(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.

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)? 

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.

lukeskylicker · Answer

Can you give me the graph of f(x)?

aryana_maria2323 · Answer

This is what the graph looks like @lukeskylicker

lukeskylicker · Answer

Do you know what a point of inflection is?

aryana_maria2323 · Answer

no not really. this entire question is throwing me off. @lukeskylicker

lukeskylicker · Answer

A point of inflection is where a graph curves to the point where it appears to be going straight and then goes back in the direction it was going.

lukeskylicker · Answer

|dw:1457641738834:dw|

aryana_maria2323 · Answer

Okay so this graph does have a point of inflection

lukeskylicker · Answer

No it does not. This is a so called "Bell curve" Where it goes up or down. Met's a minimum or maximum and then goes in the direction it came from.

aryana_maria2323 · Answer

Okay so since it does not have a inflection it can't be answer two so it must be answer one?

aryana_maria2323 · Answer

@lukeskylicker

lukeskylicker · Answer

You got it. Also sorry about the late response I had to leave.