Question

x -11 -10 -8 -4 -3 -1
g(x) 60 73 85 77 86 73
what is the best estimate for g(-7) we can make based on this table?
choose 1 answer:
a 81
b -2
c -8
d 1.3

Explanation:

Step1: Recall derivative approximation

The derivative $g^{\prime}(a)$ can be approximated by the average rate of change $\frac{g(x_2)-g(x_1)}{x_2 - x_1}$ for $x_1$ and $x_2$ close to $a$. For $a=-7$, we can use $x_1=-8$ and $x_2=-4$.

Step2: Calculate the average rate of change

We have $x_1=-8$, $g(x_1) = 85$, $x_2=-4$, $g(x_2)=77$. Then the average - rate of change is $\frac{g(-4)-g(-8)}{-4-(-8)}=\frac{77 - 85}{-4 + 8}=\frac{-8}{4}=-2$.

Answer:

B. $-2$