Suppose that f has a positive derivative for all values of x and that f(2)=0. Which of the following statements must be true of the function g(x)=ingral upper lim x lower lim 0 f(t)dt?

A. The function g has a local maximum at x=2
B. The function g has a local minimum at x=2
C. The graph of g has an inflection point at x=2
D. The graph of g crosses the x axis at x=2

Question

Suppose that f has a positive derivative for all values of x and that f(2)=0. Which of the following statements must be true of the function g(x)=ingral upper lim x lower lim 0 f(t)dt?

A. The function g has a local maximum at x=2
B. The function g has a local minimum at x=2
C. The graph of g has an inflection point at x=2
D. The graph of g crosses the x axis at x=2

anonymous · Answer

$$g(x)=\int\limits_{0}^{x}f(t)dt$$

anonymous · Answer

I'm thinking it is A but could it be D?

anonymous · Answer

It's curious, but I find it weird that f(2) = 0 is positive.
In any case, the slope is never negative, but at this point it is zero.

anonymous · Answer

Think of a curve that always rises, except at this point it is momentarily with slope zero.

anonymous · Answer

So it is straight so it would be an inflection point then

anonymous · Answer

I believe that is correct.

anonymous · Answer

ok....good explanation thanks.