Question

Let g be a function of x such that g(4) = −1 and g ′(4) = 2. Find the linearization of g(4).

A 4 − 1(x − 2)
B −1 + 2(x − 4)
C 2 − (x − 4)
D −1 + 4(x − 2)

Answer 1

The linearization of the function g(x) at x=4, given that g(4) = -1 and g'(4) = 2, is -1 + 2(x - 4), which corresponds to option B.

Step-by-step explanation:

The student is asking about the linearization of the function g(x) at the point where x is 4.

To find the linear approximation of g(x) at x=4, we use the following formula based on the values given:

Linearization Formula:

L(x) = g(a) + g'(a)(x - a)

Given that g(4) = -1 and g'(4) = 2, we substitute these values into the formula, choosing a = 4:

L(x) = -1 + 2(x - 4)

This corresponds to choice B from the given options. Therefore, the linearization of the function g at x=4 is

B: -1 + 2(x - 4).