Given the function:
[tex]f(x)=3x^2-8[/tex][tex]\begin{gathered} f(x+h)=3(x+h)^2-8 \\ f(x+h)=3(x^2+2xh+h^2)-8 \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h} \\ \Rightarrow\frac{3(x^2+2xh+h^2)-8-(3x^2-8)}{h} \end{gathered}[/tex][tex]\frac{3x^2+6xh+3h^2-8-3x^2+8}{h}[/tex][tex]\frac{6xh+3h^2}{h}[/tex]
Hence, the final answer is:
[tex]\begin{gathered} \frac{3h(2x+h)}{h} \\ \Rightarrow3(2x+h) \\ \end{gathered}[/tex]
