You have the following function:
[tex]f(x)=2+4x^2[/tex]and it is necessary to simplify the expression:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Proceed as follow:
[tex]\begin{gathered} \frac{(2+4(x+h)^2)-(2+4x^2)}{h}= \\ \frac{2+4(x^2+2xh+h^2)-2-4x^2}{h}= \\ \frac{2+4x^2+8xh+4h^2-2-4x^2}{h}= \\ \frac{8xh+4h^2}{h}=\frac{8xh}{h}+\frac{4h^2}{h}=8x+4h \end{gathered}[/tex]Hence, the simplied expression is 8x + 4h
