Find the average rate of change

Question

Find the average rate of change of the function over the given interval.

f(t) = 4t + 9,      [3, 8]:

Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

left endpoint:

right endpoint:

Answer 1

The average rate of change is the slope formula,

(f(8)-f(3))/(8-3)=4.

The instantaneous rate of change is the derivative.

f'(t)=4

f'(8)=4

f'(3)=4.

The problem wants you to recognize the instantaneous rate of change at any point is equal to the average rate of change on any interval, BUT ONLY FOR A LINE. Usually these are different.