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Math Help - need help with finding points?

  1. #1
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    need help with finding points?

    Use the derivative of the function y=f(x) to find the points at which f has a local maximum, local minimum or point of inflection.

    y ' = 6(x+1)(x-2)^2

    help me with this problem, thank you
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  2. #2
    Senior Member vincisonfire's Avatar
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    You already know that *y' = 6(x+1)(x-2)^2 *
    At an extremum,  y' = 6(x+1)(x-2)^2 = 0
    That is  x\in \{-1,2\}.
    To know the nature of these points we compute the second order derivative.
     y'' = 6(x-2)^2 + 12(x+1)(x-2)= [6(x-2)+12(x+1)](x-2) =(18x)(x-2)
    If x = -1 then  y'' =-18(-3)>0 and we have a minimum.
    If x = 2 then  y'' = 0 and we have a point of inflection.
    We also have a point of inflection at x=0 because  y'' = (18\cdot 0)(0-2)=0 .
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