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

Explanation:

Step1: Recall rate - of - change formula

The instantaneous rate of change of a function at a point is the slope of the tangent line at that point. For a linear - looking part of the curve 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 curve close to \(x = 3\). We can take the point \((2,6)\) and \((3,12)\).

Step3: Calculate the slope

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \(x_1 = 2,y_1 = 6,x_2=3,y_2 = 12\). Then \(m=\frac{12 - 6}{3 - 2}=\frac{6}{1}=6\).

Answer:

6