## anonymous 3 years ago a 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

1. anonymous

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

2. anonymous

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.

3. anonymous

but what if it isn't because the question says "of the function"

4. anonymous

if there is a positive for all x doesnt that mean it never crosses x axis?

5. anonymous

positive derivative means that the curve is proceeding in downward direction

6. anonymous

oh

7. anonymous

still think its d?

8. anonymous

no no wait ..

9. anonymous

10. anonymous

now im more confused

11. anonymous

f(2)=0 implies that for f at x=2, y=0 thus option D is right.

12. anonymous

you think its d sama?

13. anonymous

Nothing can be said about the other options as there is no mention of the nature of the derivative of f except that it is +ve which implies f is always increasing in the domain. So yes it is D :)

14. anonymous

ok thanks sama and soul

15. anonymous

hope its correct

16. anonymous

Will be right ;) And you're welcome!

17. anonymous

b..is correct sorry .. see as

18. anonymous

Dude I'm so sorry! I read g as f :P B is right!