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Math Help - Maxima and Minima

  1. #1
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    Maxima and Minima

    Consider the functionn, find the critical points of f(x) and determine the local maxima and minima. (give both x and y coordinates) on the given interval. part (b) Find the absolute maxima and minima of f(x)(give both x and y coordinates) on the given interval.

    f(x)=x^3-6x^2+9x+2 on the interval [-1,4]

    For this problem, I took the derivative of f(x).
    f'(x)=3x^2-12x+9
    Then i Made a table and plugged in all the numbers within -1-4. Then i'm stuck.
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  2. #2
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    Quote Originally Posted by Esthephane View Post
    f'(x)=3x^2-12x+9
    You need to find the zeros of f'(x).
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  3. #3
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    How to I find the 0's? f'(0)?
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  4. #4
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    Quote Originally Posted by Esthephane View Post
    How to I find the 0's? f'(0)?
    What happens at critical points? At a critical point, f'(x) = 0. So to find them, we find f'(x) (which you have already done), set it equal to zero, and then solve for x. The zeros of f'(x) are the roots of f'(x), i.e. when 3x^2-12x+9= 0. Can you find the two roots of the quadratic equation?
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