Average rate of change and secant lines practice problems
Average rate of change over an interval, the slope of the secant line, and average velocity. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Find the average rate of change of \( \displaystyle f(x) = 4 x^{2} + 3 x + 3 \) on \( \displaystyle [3, 4] \), and the equation of the secant line through the endpoints.
Find the average rate of change of \( \displaystyle f(x) = 2 x^{3} + 2 x^{2} + 2 x + 1 \) on \( \displaystyle [-2, 5] \), and the equation of the secant line through the endpoints.
Find the average rate of change of \( \displaystyle f(x) = - x^{3} + x^{2} + 2 x + 2 \) on \( \displaystyle [-1, 1] \), and the equation of the secant line through the endpoints.
Find the average rate of change of \( \displaystyle f(x) = 3 x^{2} + x \) on \( \displaystyle [1, 5] \), and the equation of the secant line through the endpoints.
A ball's height after \( \displaystyle t \) seconds is \( \displaystyle s(t) = - 16 t^{2} + 70 t + 14 \) feet. Find its average velocity over \( \displaystyle 0 \le t \le 3 \).
Find the average rate of change of \( \displaystyle f(x) = 6 \sqrt{x} \) on \( \displaystyle [9, 16] \), and the equation of the secant line through the endpoints.
Find the average rate of change of \( \displaystyle f(x) = - x^{3} + 2 x^{2} - x + 1 \) on \( \displaystyle [-1, 1] \), and the equation of the secant line through the endpoints.
A ball's height after \( \displaystyle t \) seconds is \( \displaystyle s(t) = - 16 t^{2} + 45 t + 88 \) feet. Find its average velocity over \( \displaystyle 2 \le t \le 4 \).
Find the average rate of change of \( \displaystyle f(x) = - x^{3} - x^{2} - x + 1 \) on \( \displaystyle [-3, 5] \), and the equation of the secant line through the endpoints.
Find the average rate of change of \( \displaystyle f(x) = - x^{3} - 2 x^{2} - 1 \) on \( \displaystyle [1, 2] \), and the equation of the secant line through the endpoints.