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Math Help - critical points of a function

  1. #1
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    critical points of a function

    Let y = −2x^3 + 3x^2 − 3.
    Find and classify all critical points of y. Sketch the function, showing all important points.

    Just wondering what the critical points are? Are the the max and min's of the function?

    Cheers
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  2. #2
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    Quote Originally Posted by smplease View Post
    Let y = −2x^3 + 3x^2 − 3.
    Find and classify all critical points of y. Sketch the function, showing all important points.

    Just wondering what the critical points are? Are the the max and min's of the function?

    Cheers
    They're the points where dy/dx = 0, that is, stationary points.
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  3. #3
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    Quote Originally Posted by smplease View Post
    Let y = −2x^3 + 3x^2 − 3.
    Find and classify all critical points of y. Sketch the function, showing all important points.

    Just wondering what the critical points are? Are the the max and min's of the function?
    Critical points, as Mr. Fantastic pointed out, include those values of x where f'(x)=0.

    f(x)=-2x^3+3x^2-3

    f'(x)=-6x^2+6x

    f'(c)=0

    0=-6c^2+6c

    c={0,1}

    So, the critical points are (0,-3) and (1,-2).

    It's not relevant for this particular function, but critical numbers also include those values of x where f(x)∈ℝ and f'(x) is undefined.
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