Average rate of change vs. instantaneous rate of change

By Tutor GuyNo Comments

 

The average rate of change on an interval is the slope of the secant line on that interval. The instantaneous rate of change at a point is the slope of the tangent line.

Example: In the picture below, the blue curve is f(x). The red segment is the secant line between x = 1 and x = 4. The slope of this line is the average rate of change between 1 and 4. The green line is the tangent line to the curve at x = 2. Its slope is the instantaneous rate of change of f(x) at x = 2.

 

 

 

 

 

 

 

 

 

 

 

 

 

To find the average rate of change between 1 and 4, determine the coordinates of the endpoints of the red secant line and calculate the slope. To find the instantaneous rate of change at x = 2, calculate f’(2).

Calculus
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