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)
Stacey Warren - Expert brainly.com
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Is A. where you have to find where f(x) is increasing?
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?
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:
I think your only problem here is the vocabulary. This tells you what relative and absolute extrema are. You can take it from there :)