Question

A ball is thrown upward from the top of a building the function below shows the height of the ball in relation to sea level f(t) = -16t^2 +32t+90 The average rate of change of f(t) from t=4 seconds to t=6 seconds is ____ feet per second

Answer 1

$\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ f(t) = -16t^2 +32t+90\quad \begin{cases} t_1=4\\ t_2=6 \end{cases}\implies \cfrac{f(6)-f(4)}{6-4}$