Answer:
the average rate of change rc is 13 , 12.1 and 12.01 for h=1 , 0.1 and 0.01 respectively
Step-by-step explanation:
for
R(t) = 30*t − 3*t² ; t = 3
the average rate of change of R(t) over the time interval [t, t + h] is
rc= [R(t+h)-R(t)] / [(t+h) -t) = [R(t+h)-R(t)] /h = 1/h * [ 30*(t+h) − 3*(t+h)² - ( 30*t − 3*t² ) ] = (1/h) * ( 30*h - (3*t² + 6*t*h + t²) +3*t² ) = 30 - 6*t + h
then
rc= 30 - 6*t + h
for t=3 and h=1
rc= 30 - 6*3 + 1 = 13
for t=3 and h=0.1
rc= 30 - 6*3 + 0.1 = 12.1
for t=3 and h=0.01
rc= 30 - 6*3 + 0.01 = 12.01
for t=3 and h=0.001
rc= 30 - 6*3 + 0.01 = 12.001
when h goes smaller , the average rate of change gets closer to the instantaneous rate of change of R(t) in t=3 (the derivative of R in t=3) , that is
R'(t)= 30 - 6*t
