Find the average rate of change for f(t)=5t^2+8 over the interval [2,2+h].

Answer 1

Average rate of change = [f(2+h) - f(2)] / h = [5(2+h)² + 8 - (5(2)² + 8)] / (2+h - 2)

= [5(4 + 4h + h²) - 20] / h = (20h + 5h²) / h = h(20 + 5h) / h = 20 + 5h