The graph of f ′(x) is continuous and increasing with an x-intercept at x = 5. Which of the following statements must be true?

The graph of f is always concave up.
The graph of f has an inflection point at x = 5.
The graph of f has a relative maximum at x = 5.
None of these is true.

Question

The graph of f ′(x) is continuous and increasing with an x-intercept at x = 5. Which of the following statements must be true?

 The graph of f is always concave up.
 The graph of f has an inflection point at x = 5.
 The graph of f has a relative maximum at x = 5.
 None of these is true.

anonymous · Answer

I think it is "a"?

anonymous · Answer

First derivative will not tell you about concavity

anonymous · Answer

It will tell you of potential min and max values at its roots

anonymous · Answer

If the derivative is increasing when it goes through the x axis, that means there is likely a minimum at that point.

anonymous · Answer

If it is decreasing, this would mean a maximum

anonymous · Answer

So which one is it?

anonymous · Answer

Think about it for a moment based on what I said

anonymous · Answer

5 would be a minimum?

anonymous · Answer

Yes

anonymous · Answer

So which answer selection do you have to chose?

anonymous · Answer

That's what I got the first time, so I chose "d" and I got it wrong. I am going and redoing the ones I got wrong before my test lol