[tex]f(x)=-4x^2+7x+4[/tex][tex]\begin{gathered} f(x+h)=-4(x+h)^2+7(x+h)+4 \\ f(x+h)=-4(x^2+2xh+h^2)+7x+7h+4 \\ f(x+h)=-4x^2-8xh-4h^2+7x+7h+4 \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-8xh-h^2+7x+7h+4-(-4x^2+7x+4)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{7h-8xh-h^2}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(7-8x-h)}{h} \\ \frac{f(x+h)-f(x)}{h}=7-8x-h \end{gathered}[/tex]
