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Math Help - Exponential function

  1. #1
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    Exponential function

    How to complete the following table?

    And also:
    a) f(x) = 2x^3 + 3x^2 - 12x + 6 has critical points at x = -2 and x = 1. Use the second derivative test to determine whether these are local maximum or local minimum values.

    b)
    how to Calculate f(-2) and f(1) . Briefly explain the appropriateness of these two values
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Snowboarder View Post
    How to complete the following table?

    And also:
    a) f(x) = 2x^3 + 3x^2 - 12x + 6 has critical points at x = -2 and x = 1. Use the second derivative test to determine whether these are local maximum or local minimum values.

    b) how to Calculate f(-2) and f(1) . Briefly explain the appropriateness of these two values
    f(x) = 2x^3 + 3x^2 - 12x + 6

    taking the derivative we get

    f'(x)=6x^2+6x-12=6(x^2+x-2)=6(x+2)(x-1)

    So our critical points are -2 and 1

    now taking the 2nd derivative we get

    f''(x)=12x+6

    Now we check the above critical points

    f''(-2)=12(-2)+6=-18 so this is a max

    f''(1)=12(1)+6=18 so this is a min.

    Good luck.
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