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?
Options: 5.1, 5.2, 5.3, or 5.4​

Answer 1

Answer:

5.2

Step-by-step explanation:

g(x) = mx +b

g'(x) = m = 2 for all x

g(-1) = 2(-1) + b = 5

-2 + b = 5

b = 7

So, g(x) = 2x + 7

Therefore g(-.9) = 2(-.9) + 7

= -1.8 + 7 = 5.2