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anonymous

  • 5 years ago

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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  1. anonymous
    • 5 years ago
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    Is A. where you have to find where f(x) is increasing?

  2. anonymous
    • 5 years ago
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    Yes

  3. anonymous
    • 5 years ago
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    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.

  4. anonymous
    • 5 years ago
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    Can you do any of A or B given that information?

  5. anonymous
    • 5 years ago
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    Yes! Thanks!

  6. anonymous
    • 5 years ago
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    Good!

  7. anonymous
    • 5 years ago
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    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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