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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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\[g(x)= \int\limits_{0}^{x}f(t) dt\]
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.
but what if it isn't because the question says "of the function"

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Other answers:

if there is a positive for all x doesnt that mean it never crosses x axis?
positive derivative means that the curve is proceeding in downward direction
still think its d?
no no wait ..
i think its b,c,d .. comments please :)
now im more confused
f(2)=0 implies that for f at x=2, y=0 thus option D is right.
you think its d sama?
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 :)
ok thanks sama and soul
hope its correct
Will be right ;) And you're welcome! correct sorry .. see as
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Dude I'm so sorry! I read g as f :P B is right!

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