Calculus question

Question

Consider the following function.

f(t) = 6t² − 3

Find the average rate of change of the function below over the interval [5, 5.1].

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

 (at t = 5)

 (at t = 5.1)

Answer 1

f(5.1) = 6*5.1^2 -3 = 6*26.01-3 = 153.06

f(5) = 6*5^2 - 3 = 6*25-3 = 150-3 = 147

[f(5.1)-f(5)]/ (5.1 - 5)

[153.06 - 147]/ 0.1

= 6.06 / 0.1

= 60.6