AP Calculus Differentiation: Velocity and Other Rates of Change

We have already seen that the instantaneous rate of change is the same as the slope of the tangent line and thus the derivative at that point. Unless we use the phrase "average rate of change," we will assume that in calculus, the phrase "rate of change" refers to the instantaneous rate of change.

 

Example 1: The length of a rectangle is given by 2t\:+1 and its height is , where  is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time, and indicate the units of measure for this rate.

 

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