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 your estimate needs to be within 10% of the exact answer. question help: video message instructor submit question

Explanation:

Step1: Recall rate - of - change formula

The instantaneous rate of change of a function at a point is approximated by the slope of the tangent line at that point. We can estimate the slope using two nearby points.

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

Let's choose the points \((2,6)\) and \((3,12)\) (read from the graph as approximately).

Step3: Calculate the slope

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 2,y_1=6,x_2 = 3,y_2 = 12\). So \(m=\frac{12 - 6}{3 - 2}=\frac{6}{1}=6\).

Answer:

6