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)

Question

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)

anonymous · Answer

Is A. where you have to find where f(x) is increasing?

anonymous · Answer

Yes

anonymous · Answer

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.

anonymous · Answer

Can you do any of A or B given that information?

anonymous · Answer

Yes! Thanks!

anonymous · Answer

Good!

anonymous · Answer

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 :)