An object is thrown up. Its height is given by y(t) = 100t − 16t2

Question

An object is thrown straight up. Its height is given by

y(t) = 100t − 16t²

with y in feet and t in seconds. Write a formula for the average velocity on the interval[2, 2 + h].

 Enter your answer as an algebraic expression. You do not have to simplify.

Δy

Δt = ________

Answer 1

The average rate change of a function over an interval is the change in the position divided by the change in time.

Average Rate of Change = (y(2+h) - y(2)) / ((2+h) - 2) = (y(2+h) - y(2)) / h

y(2) = 100(2) - 16(2)² = 200 - 64 = 136

y(2+h) = 100(2+h) -16(2+h)²

Average Rate of Change = ((100(2+h) - 16(2+h)² -136) / h