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

Question

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

anonymous · Answer

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

anonymous · Answer

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

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

anonymous · Answer

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

anonymous · Answer

positive derivative means that the curve is proceeding in downward direction

anonymous · Answer

oh

anonymous · Answer

still think  its d?

anonymous · Answer

no no wait ..

anonymous · Answer

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

anonymous · Answer

now im more confused

anonymous · Answer

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

anonymous · Answer

you think its d sama?

anonymous · Answer

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 :)

anonymous · Answer

ok thanks sama and soul

anonymous · Answer

hope its correct

anonymous · Answer

Will be right ;) And you're welcome!

anonymous · Answer

b..is correct sorry ..
see as

anonymous · Answer

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