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Math Help - Finding local minimum, local maximum or neither

  1. #1
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    Finding local minimum, local maximum or neither

    So I'm trying to find the local minimum, maximum or neither for the following function:

    f(x)=(x-1)^2 * (x+3)^2

    I've already found the stationary points (1,0), (-1,16), (-3,0)

    So do I plug the x values into the second derivative which is 12x^2 + 24x - 4

    so for example (12*1)^2 + (24*1) - 4 = 164 which means it is local minimum

    (12*-1)^2 + (24*-1) - 4 = 116 which means a local minimum

    and (12*-3)^2 + (24*-3) - 4 = 1,220 which is also a local minimum...

    I feel this is wrong though. Can someone give me some guidance?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    For x=-3 or x=1 , local minimum, for x=-1 , local maximum.
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  3. #3
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    Can you please show how you got those answers? Did you do the second derivative test like I did?
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  4. #4
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    Quote Originally Posted by brumby_3 View Post

    So do I plug the x values into the second derivative which is 12x^2 + 24x - 4

    so for example (12*1)^2 + (24*1) - 4 = 164 which means it is local minimum

    (12*-1)^2 + (24*-1) - 4 = 116 which means a local minimum

    and (12*-3)^2 + (24*-3) - 4 = 1,220 which is also a local minimum...
    Yes you plug those x-values into the second derivative, however you are squaring the 12 in this equation.

    you are doing this: (12x)^2
    instead of this: 12(x^2)
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  5. #5
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    Thanks for the help, I understand now
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