Let g be a differentiable function with g(-1) = 5 and g'(-1) = 2. What is the value of the approximation of...

Question

Let g be a differentiable function with g(-1) = 5 and g'(-1) = 2.
What is the value of the approximation of g(-0.9) using the function's local linear approximation at x = -1?
Choose 1 answer:
A) 5.1
B) 5.2
C) 5.3
D) 5.4

SnapAndSolve AI · Accepted Answer

To find the local linear approximation of g(-0.9) at x = -1, we use the formula for linear approximation:

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

Here, a = -1, g(a) = 5, and g'(a) = 2. We want to approximate g(-0.9):

L(-0.9) = 5 + 2(-0.9 + 1)

L(-0.9) = 5 + 2(0.1)

L(-0.9) = 5 + 0.2

L(-0.9) = 5.2

The correct answer is B) 5.2

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Let g be a differentiable function with g(-1) = 5 and g'(-1) = 2. What is the value of the approximation of...

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