If g(x) is increasing on the interval [-5,10), which of the following could be true?

A. g(x) has a relative minimum at x = 2.
B g(x) has no relative extrema.
C g(x) has a relative minimum at x = 10.
D g(x) has a relative maximum at x = 10.

Question

If g(x) is increasing on the interval [-5,10), which of the following could be true?

A.		g(x) has a relative minimum at x = 2.
B		g(x) has no relative extrema.
C		g(x) has a relative minimum at x = 10.
D		g(x) has a relative maximum at x = 10.

anonymous · Answer

the question says which COULD BE TRUE.

anonymous · Answer

look at the answer choices.

a.- x=2 is within the given interval. the question states that in this interval the function is increasing. so can x=2 be a relative minimum. Hint : would the function be more or less at x=1 than at x=2?

anonymous · Answer

more at x=2?

anonymous · Answer

yes. so it is increasing through but not including x=10

anonymous · Answer

so D?

anonymous · Answer

if you a function f(x) which is strictly increasing in an an interval then f'(x) will never be zero.therefore one thing is sure that there is no x which belongs to[-5,10) at which we will get a minima or maxima.so now we are left only with the end points.now think what should be your next step

zarkon · Answer

I don't think the assumption that f'(x) exists (or that f is continuous) should be made since it is not stated as such.