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Math Help - Family of Functions!

  1. #1
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    Family of Functions!

    let p(x) = x^3-ax, where a is constant

    a.) if a<0, show that p(x) is alwayss increasing
    b.) if a>0, show that p(x) has a local maximum and minimum
    c.) sketch and label typical graphs for the cases when a<0 and when a>0

    can i get some help with this one please, i just dont know what to do...thanks

    mathlete
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathlete View Post
    let p(x) = x^3-ax, where a is constant

    a.) if a<0, show that p(x) is alwayss increasing
    find the derivative, show that it will always be positive

    b.) if a>0, show that p(x) has a local maximum and minimum
    set the derivative you found in part (a) to 0 and solve for x. you will get two solutions. note that a must be positive for the solutions to work.

    c.) sketch and label typical graphs for the cases when a<0 and when a>0
    it shouldn't be hard coming up with examples. just plug in a number for a>0 and graph that, then plug in a number for a<0 and graph that. the families of curves should all look familiar
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