we have the function
[tex]f(x)=-3x^2-6x+1[/tex]
Find out f(x+h)
[tex]\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}[/tex][tex]\begin{gathered} f(x+h)=-3x^2-6xh-3h^2-6x-6h+1 \\ \end{gathered}[/tex]
substitute in the difference quotient
[tex]\frac{-3x^2-6xh-3h^2-6x-6h+1-(-3x^2-6x+1)}{h}[/tex]
Combine like terms
[tex]\frac{^{}-6xh-3h^2-6h}{h}[/tex][tex]-6x-3h-6[/tex]
