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Math Help - Local Extrema

  1. #1
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    Local Extrema

    Started doing local extrema which concepts I understand. I am struggling with two problems which I was hoping to get some help on. The problem states to find the critical points and local min and max. I know to take first and second derivative to find the values but thats where i am messing up. Thanks for the help.

    9) h(y)= y2 - 1/y

    15) f(x)= pi - (x-2)​2/3
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  2. #2
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    Re: Local Extrema

    9) h(y)= y2 - 1/y

    Remember 1/y= y-1
    The derivative of 1/y is therefore -1y-2
    The derivative of y2 is 2y
    You can then solve 2y - (-1y-2)= 0 for y

    15) f(x)= pi - (x-2)​2/3
    Since pi is a constant the derivative of pi is 0
    The derivative of (x-2)2/3 is (2/3)(x-2)-1/3
    So you can solve -(2/3)(x-2)-1/3= 0 for x
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