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Math Help - Critical Points

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    Smile Critical Points

    x^3(2x-7)^2(x+5)=0


    I don't know how to solve this and I need this part so I can find the local max and min.
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  2. #2
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    Quote Originally Posted by lisa1984wilson View Post
    x^3(2x-7)^2(x+5)=0


    I don't know how to solve this and I need this part so I can find the local max and min.
     <br />
x^3(x+5)(2x-7)^2=0<br />

    f(x)=(x^4+5x^3)(2x-7)^2=0

    differentiate wrt x using product rule,

    (x^4+5x^3)2(2x-7)+(4x^3+15x^2)(2x-7)^2=0

    x^2(2x-7)[2(x^2+5x)+(4x+15)(2x-7)]

    x^2(2x-7)(2x^2+10x+8x^2+2x-105)

    f'(x)=x^2(2x-7)(10x^2+12x-105)=0
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  3. #3
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by lisa1984wilson View Post
    x^3(2x-7)^2(x+5)=0


    I don't know how to solve this and I need this part so I can find the local max and min.
    x^3(x+5)(2x-7)^2=0
    It's either x^3, (x+5) or (2x-7)^2 that is worth 0. Solve for x.

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