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Calculus(Urgent help)

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f(x)=x^3-3x^2+3x+1 near 2 (at a=2)

A. Use Linear approximation to approximate.
b.is this underestimate or overestimate? Justify answer.
C.Approximate f(2.25) using the linear approximation and compare the answer with the exact value.


Thanks.

  • Calculus(Urgent help) -

    f'(x) = 3x^2 - 6x + 3
    f''(x) = 6x - 6

    f''(2) > 0, so the graph is concave up at x=2. So, a linear approximation will underestimate f(x)

    f'(2) = 3
    f(2) = 3
    the line through (2,3) with slope 3 is

    y = 3(x-2)+3= 3x-3

    y(2.25) = 3.75
    f(2.25) = 3.953
    the line underestimates

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