Question

s of a function using local linearity and linearization quiz (mcqs)
2 mark for review
selected values of the derivative of the function g are given in the table above. it is known that g(3) = 17
what is the approximation for g(3.2) found using the line tangent to the graph of g at x = 3?
a 16.76
b 16.80
c 16.84
d 17.40

Explanation:

Step1: Recall the linear approximation formula

The linear approximation formula is \(L(x)=g(a)+g^{\prime}(a)(x - a)\). Here, \(a = 3\), \(x=3.2\), \(g(3)=17\), and from the table \(g^{\prime}(3)=- 1.2\).

Step2: Substitute values into the formula

Substitute \(a = 3\), \(x = 3.2\), \(g(3)=17\), \(g^{\prime}(3)=-1.2\) into \(L(x)=g(a)+g^{\prime}(a)(x - a)\). We get \(L(3.2)=g(3)+g^{\prime}(3)(3.2 - 3)\).

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Answer:

\(16.76\), so the answer is A.