MA.912.C.3.8

Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed and acceleration.

Examples

Example: The vertical distance traveled by an object within the earth’s gravitational field, neglecting air resistance, is given by the equation x=0.5gt² + v_ot + x_o, where g is the force on the object due to earth's gravity, v_o is the initial velocity, x₀ is the initial height above the ground, t is the time in seconds and down is the negative vertical direction. Determine the instantaneous speed and the average speed for an object, initially at rest, 3 seconds after it is dropped from a 100 m. tall cliff. Describe the object 5 seconds after it is dropped from the same height. Use .