Math

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Find f.
f ''(x) = 20x3 + 12x2 + 10,    f(0) = 9,    f(1) = 12

  • Math -

    integrating once to get
    f'(x) = 5x^4 + 4x^3 + 10x + c
    check by taking the derivative,

    integrate once more to get
    f(x) = x^5 + x^4 + 5x^2 + cx + k

    now use the two given points:
    for f(0) =9
    9 = 0+0+0+0+k , so k = 9
    for (1,12)
    12 = 1+1+5+c+9
    c = ...

    f(x) = ....

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