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.

Answer 1

I think it is "a"?

Answer 2

First derivative will not tell you about concavity

Answer 3

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

Answer 4

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

Answer 5

If it is decreasing, this would mean a maximum

Answer 6

So which one is it?

Answer 7

Think about it for a moment based on what I said

Answer 8

5 would be a minimum?

Answer 9

Yes

Answer 10

So which answer selection do you have to chose?

Answer 11

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