Please help! Will FAN AND MEDAL!

The graph of f ′(x) is continuous and increasing with an x-intercept at x = 4. Which of the following statements must be true?

a. The graph of f is always concave down.
b. The graph of f is always increasing.
c. The graph of f has a relative minimum at x = 4.
d. The graph of f has an inflection point at x = 4.

Question

Please help! Will FAN AND MEDAL! 

The graph of f ′(x) is continuous and increasing with an x-intercept at x = 4. Which of the following statements must be true?

a. The graph of f is always concave down.
b. The graph of f is always increasing.
c. The graph of f has a relative minimum at x = 4.
d. The graph of f has an inflection point at x = 4.

aryana_maria2323 · Answer

Can you please help? @agent0smith @Directrix @ganeshie8 @Kainui @Nnesha

agent0smith · Answer

I'd start by drawing a basic graph of f'. 

Always increasing means it has a positive slope (doesn't matter what, just a positive slope), and it has an x-int at x=4.

aryana_maria2323 · Answer

since it is positive does it mean it has a minimum right?

agent0smith · Answer

There will be a minimum where f' goes from negative to positive.

aryana_maria2323 · Answer

so will it have a relative minimum at x=4?

agent0smith · Answer

Yes

aryana_maria2323 · Answer

Okay so since that is true I am guessing that will be the answer. C?

agent0smith · Answer

Yes

aryana_maria2323 · Answer

Can you help me with two more? @agent0smith

agent0smith · Answer

Sorry, I'm leaving

aryana_maria2323 · Answer

Okay no worries.