Average rate of change over an interval

(a)  

 $f\left(x\right)=-2x^2+2x-2;\left[-1,1\right]$  

(a)  

 $f\left(x\right)=2x^2-x-2;\left[1,2\right]$  

Find the average rate of change of the function over the given interval.

(a)  

 $f\left(x\right)=-x^2-x-1;\left[-2,-1\right]$  

(a)  

 $f\left(x\right)=-\frac{1}{x};\left[2,3\right]$  

(a)  

 $f\left(x\right)=\frac{1}{x-1};\left[-4,-3\right]$  

(a)  

An astronaut drops a rock off the edge of a cliff on the Moon. The distance, d(t), in meters, the rock travels after t seconds can be modeled by the function  $d\left(t\right)=0.8t^2$  . What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?


(a)  

What is the average rate of change from [1, 5]?

(a)  

A soccer ball is dropped from the top of a gym. It's height  $H$ in feet is given by the function  $H=-16T^2+125$ , where  $T$  is measured in seconds.  Find the average speed of the ball, in feet per second, for the time interval  $\left[0.5,\ \ 2.5\right]$ .   

(a)