Question

Find the difference quotient , where , for the function below.

Answer 1

we have the function

`f(x)=-3x^2-6x+1`

Find out f(x+h)

`\begin{gathered} f(x+h)=-3(x+h)^2-6(x+h)+1 \\ f(x+h)=-3(x^2+2xh+h^2)-6x-6h+1 \end{gathered}`
`\begin{gathered} f(x+h)=-3x^2-6xh-3h^2-6x-6h+1 \\ \end{gathered}`

substitute in the difference quotient

`(-3x^2-6xh-3h^2-6x-6h+1-(-3x^2-6x+1))/(h)`

Combine like terms

`\frac{^{}-6xh-3h^2-6h}{h}`
`-6x-3h-6`