Calculus Help Please

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Use a linear approximation (or differentials) to estimate the given number.

(1.999)^4

  • Calculus Help Please -

    f(x) = f(a) + (x-a) f'(a)

    f(x) = x^4
    df/dx = 4x^3

    let a = 2
    then f(a) = 2^4 = 16
    f'(a) = 4*8 = 32

    f(x) = 16 + (x-a)(32)
    x-a = - .001
    so
    f(1.999) = 16 -.001(32) = 16 - .032
    f(1.999) = 15.968

    with calculator it is 15.968 also

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