Question

estimate the instantaneous rate of change at x = 2. your estimate needs to be within 10% of the exact answer. (contact help: ① video ② message instructor) submit question

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.

Step2: Estimate tangent slope

To estimate the slope of the tangent line at \(x = 2\), we can pick two points close to the tangent line near \(x = 2\). Let's choose the points \((1.5,5)\) and \((2.5,9)\) (estimated from the graph).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1 = 1.5,y_1 = 5,x_2 = 2.5,y_2 = 9\).
\[m=\frac{9 - 5}{2.5-1.5}=\frac{4}{1}=4\]

Answer:

4