You are camping at the Grand Canyon. When you pitch your tent at 1:00 P. M. the temperature is 81° F. When you go to bed at 11 P.M. the temperature is 61° F. What is the average rate of change in the temperature?

Question

You are camping at the Grand Canyon.  When you pitch your tent at 1:00 P. M. the temperature is 81° F.  When you go to bed at 11 P.M. the temperature is 61° F.  What is the average rate of change in the temperature?

anonymous · Answer

$$\frac{61-81}{11-1}=\frac{-20}{10}=-2$$

anonymous · Answer

x - a represents the change in the input of the function f
f(x) - f(a) represents the change in the function f as the input changes from a to x
then the average rate of change A(x) is$$A(x)=\frac{f(x)-f(a)}{x-a}$$