Question

score on last try: 0 of 1 pts. see details for more.> next question get a similar question you can retry this question below estimate the instantaneous rate of change at x = 3

Explanation:

Step1: Recall rate - of - change concept

The instantaneous rate of change of a function at a point is the slope of the tangent line at that point. For a linear - like part of the graph near \(x = 3\), we can estimate the slope using the formula \(m=\frac{\Delta y}{\Delta x}\).

Step2: Select two points near \(x = 3\)

Let's choose two points on the line near \(x = 3\). Suppose we choose \((2,7)\) and \((3,10)\) (by observing the graph).

Step3: Calculate the slope

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)=(2,7)\) and \((x_2,y_2)=(3,10)\). Then \(m=\frac{10 - 7}{3 - 2}=\frac{3}{1}=3\).

Answer:

3