the function g is differentiable and satisfies g(-1) = 4 and g(-1) = 2. what is the approximation of g(-1.2)…

the function g is differentiable and satisfies g(-1) = 4 and g(-1) = 2. what is the approximation of g(-1.2) using the line tangent to the graph of g at x = -1? a 3.6 b 3.8 c 4.2 d 4.4

the function g is differentiable and satisfies g(-1) = 4 and g(-1) = 2. what is the approximation of g(-1.2) using the line tangent to the graph of g at x = -1? a 3.6 b 3.8 c 4.2 d 4.4

Answer

Explanation:

Step1: Recall linear - approximation formula

The linear - approximation formula is $L(x)=g(a)+g^{\prime}(a)(x - a)$, where $a=-1$ and $x=-1.2$.

Step2: Substitute values into the formula

We know that $g(a)=g(-1) = 4$, $g^{\prime}(a)=g^{\prime}(-1)=2$, and $x - a=-1.2-(-1)=-0.2$. Then $L(-1.2)=g(-1)+g^{\prime}(-1)(-1.2 - (-1))$.

Step3: Calculate the approximation

$L(-1.2)=4+2\times(-0.2)=4 - 0.4=3.6$.

Answer:

A. 3.6