Suppose that f(x)f(x) is a function with f(155)=52f(155)=52 and f′(155)=4f′(155)=4. Estimate f(160)f(160).

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13-02-2017
Mathematics

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Suppose that f(x)f(x) is a function with f(155)=52f(155)=52 and f′(155)=4f′(155)=4. Estimate f(160)f(160).

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LammettHash LammettHash · Answer 1 · 2017-02-13T10:45:36-05:00

LammettHash LammettHash

13-02-2017

By the mean value theorem, the linear approximation of a function around \(x=a\) is

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

so the desired approximation can be computed with

\(f(160)\approx f(155)+f'(155)(160-155)=72\)

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