Given the following function f(x)=x^3-6x^2+15, on the interval(s) where f(x) is increasing. B. Where f(x) is decreasing. C. Determine the extreme points and classify them as relative and/or absolute maximum(s) or minimum(s)

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Given the following function f(x)=x^3-6x^2+15, on the interval(s) where f(x) is increasing. B. Where f(x) is decreasing. C. Determine the extreme points and classify them as relative and/or absolute maximum(s) or minimum(s)

Mathematics
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Is A. where you have to find where f(x) is increasing?
Yes
Okay, the gradient function tells you everything you need to know. You know that a line is increasing when it has positive slope. The slope of a function is given by f'(x). So when f'(x) is positive (i.e. greater than zero), the set of x's that allow for this is the interval over which f is increasing. A similar situation exists for a decreasing function f. Here, f'(x) will be less than zero, since the slope needs to be negative. You find extrema by setting f'(x) = 0, since at the x-values that satisfy this condition, it may be the case that the function turns from positive gradient, to negative.

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Can you do any of A or B given that information?
Yes! Thanks!
Good!
As I'm too tired to do any more today, for part C, you can get the idea about what you need to do from this: http://mathforum.org/library/drmath/view/64504.html I think your only problem here is the vocabulary. This tells you what relative and absolute extrema are. You can take it from there :)

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