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iplayffxiv 2 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

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1. iplayffxiv

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

2. iplayffxiv

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. iplayffxiv

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

4. iplayffxiv

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

5. fatima1

positive derivative means that the curve is proceeding in downward direction

6. iplayffxiv

oh

7. iplayffxiv

still think its d?

8. t_soulb

no no wait ..

9. t_soulb

i think its b,c,d .. comments please :)

10. iplayffxiv

now im more confused

11. sama491

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

12. iplayffxiv

you think its d sama?

13. sama491

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. iplayffxiv

ok thanks sama and soul

15. iplayffxiv

hope its correct

16. sama491

Will be right ;) And you're welcome!

17. t_soulb

b..is correct sorry .. see as

18. sama491

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

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