Question

Using the graph, estimate the instantaneous rate of change when x=2

Answer 1

Answer:

-8

Explanation:

The instantaneous rate of change when x = 2 is equal to the slope of the tangent line at that point. So, we need to find the slope of the following line

Using two points (x1, y1) and (x2, y2) of the line, we can calculate the slope as follows

$m=\frac{y_2-y_1}{x_2-x_1}$

So, replacing (x1, y1) by (2, -8) and (x2, y2) by (1, 0), we get:

$m=\frac{0-(-8)}{1-2}=\frac{0+8}{-1}=\frac{8}{-1}=-8$

Therefore, the estimate of the instantaneous rate of change is -8.