Question

suppose that ( f(900)=4000 ) and ( f^{prime}(900)=20 ). estimate each of the following.
(a) ( f(901) ) (b) ( f(900.5) ) (c) ( f(899) )
(d) ( f(898) ) (e) ( f(899.75) )
(a) ( f(901) approx ) (simplify your answer. type an exact answer.)

Explanation:

Step1: Recall the linear approximation formula

The linear approximation formula is \(f(x)\approx f(a)+f^{\prime}(a)(x - a)\). Here \(a = 900\), \(f(a)=4000\), and \(f^{\prime}(a)=20\).

Step2: For \(f(901)\)

Substitute \(x = 901\) into the formula. Then \(x-a=901 - 900=1\).

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Answer:

\(4020\)