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Thread: 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, $\displaystyle f'(x) = 0$. So to find them, we find $\displaystyle f'(x) $ (which you have already done), set it equal to zero, and then solve for $\displaystyle x$. The zeros of $\displaystyle f'(x) $ are the roots of $\displaystyle f'(x)$, i.e. when $\displaystyle 3x^2-12x+9= 0$. Can you find the two roots of the quadratic equation?
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