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

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

the least value out of the data shown is 5, maybe if you post a picture with it i could a little more.

step-by-step explanation:

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.