iplayffxiv
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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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iplayffxiv
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\[g(x)= \int\limits_{0}^{x}f(t) dt\]
iplayffxiv
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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.
iplayffxiv
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but what if it isn't because the question says "of the function"
iplayffxiv
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if there is a positive for all x doesnt that mean it never crosses x axis?
fatima1
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positive derivative means that the curve is proceeding in downward direction
iplayffxiv
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oh
iplayffxiv
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still think its d?
t_soulb
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no no wait ..
t_soulb
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i think its b,c,d ..
comments please :)
iplayffxiv
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now im more confused
sama491
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f(2)=0 implies that for f at x=2, y=0 thus option D is right.
iplayffxiv
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you think its d sama?
sama491
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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 :)
iplayffxiv
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ok thanks sama and soul
iplayffxiv
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hope its correct
sama491
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Will be right ;) And you're welcome!
t_soulb
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b..is correct sorry ..
see as
sama491
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Dude I'm so sorry! I read g as f :P
B is right!