Brief Calculus.

Question

If an object is dropped from a tall building, then the height, in feet after t seconds is given by the function

h(t)= 200-16t^2

Find and interpret the average rate of change from t= 1 to 3 seconds.

Answer 1

The average rate of change = Δy/Δx = (y₁-y₀)/(x₁-x₀)

y₀ = h(1) = 184

y₁=h(3) = 56

x₀ = 1

x₁ = 3

Δy/Δx = -128/2 = -64 ft/sec

On average, for the interval [1,3], the object is falling at 64 ft per second.