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Find f.

f ''(x) = −2 + 12x − 12x2, f(0) = 9, f '(0) = 14

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2 answers

  1. d^2y/dx^2 = -12 x^2 + 12 x - 2
    dy/dx = - 4 x^ 3 + 6 x^2 - 2 x + c
    at = 0 dy/dx = 14 so c = 14
    dy/dx = - 4 x^ 3 + 6 x^2 - 2 x + 14
    y = - x^4 + 2 x^3 - x^2 + 14 x + d
    at 0 , y = d = 9
    so
    y = - x^4 + 2 x^3 - x^2 + 14 x + 9

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  2. almost the same as
    https://www.jiskha.com/display.cgi?id=1525996280

    keep integration to go from f''(x) to f'(x) to f(x)
    make sure you find the value of the constant in each step

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