A function is given. Determine the average rate of change of the function between the given values of the variable.

Question

A function is given. Determine the average rate of change of the function between the given values of the variable.

f(x) = 5 − x²;    x = 9, x = 9 + h

Answer 1

f(x) = 5 - x²

Average rate of change from x = 9 to x = 9+h is:

[f(9+h) - f(9)] / h = [5 - (9+h)² - (5 - 81)] / h

= [-18h - h²] / h = -18 - h