math

Determine the points on the curve y=x^2(x^3-x)^2 where the tangent line is horizontal. Thx!

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  1. (y z x2)

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  2. The slope of the tangent line is equal to the first derivative.

    You must find where is first derivative=0

    In this case the tangent line is horizontal.

    In google type: calc101

    When you see list of results click on:

    Calc101com Automatic Calculus,Linear Algebra and Polynomials

    When page be open clik option: derivatives

    When this page be open in rectacangle type your equation and click options
    DO IT

    You will see solution for first derivative.

    Then in google type: equation solver

    When you see list of results click on:

    Equation Calculator & Solver-Algebra.help

    When this page be open in rectacangle type expresion for firste derivatives=0 and click options solve.

    If your expresion is:
    x^2*(x^3-x)^2

    First derivative is:
    4(2x^7-3x^5+x^3)

    In this case in equation solver type:
    4(2x^7-3x^5+x^3)=0

    and solutions is:

    -1, -sqroot(2)/2, sqroot(2)/2, 1

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  3. One of solutions is obviously:

    x=0

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