Question

Find and simplify the difference quotient of the​ form,
`(f(x+h)-f(x))/(h) , h\\eq 0`


`f(x)=-10x+9`

`(f(x+h)-f(x))/(h) =`

Answer 1

With
`f(x)=-10x+9`, we have

`f(x+h) = -10(x+h) + 9 = -10x + 9 - 10h`

Then the difference quotient is

`\frac{f(x+h)-f(x)}h = \frac{(-10x+9-10h)-(-10x+9)}h = \frac{-10h}h = -10`

since h ≠ 0.