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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
Answer
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