Question

Average rate of change for f(x) = x2 − 3x − 10 from x = −5 to x = 10.

Answer 1

The average rate of change is the slope of the secant line connecting the points on f(x) from x=-5 to x=10.

In other words, it is just the slope of the straight line connecting the points

`(-5,f(-5)) \: and \: (10,f(10))`

So we were given ,


`f(x) = {x}^(2) - 3x - 10`

At

`x = - 5`

`f( - 5) = {( -5 )}^(2) - 3( - 5) - 10`

`f( - 5) = 25 + 15- 10`

`f( - 5) = 30`

Also at

`x = 10`

`f( 10) = {( 10)}^(2) - 3( 10) - 10.`

`f( 10) = 100- 30 - 10`

`f( 10) = 60`

The average rate of change

`= (f(10) - f( - 5))/(10 - - 5)`

`= (60- 30)/(15)`

`= (30)/(15)`

`= 2`