The average rate of change of the function over the interval (0, h) is
[tex]\frac{f(h)-f(0)}{h-0}=\frac{f(h)-f(0)}{h}[/tex]Now,
[tex]f(h)=3h^2+4h-5[/tex]and
[tex]f(0)=-5[/tex]Therefore, the average rate of change is
[tex]\frac{3h^2+4h-5-5}{h}=\textcolor{#FF7968}{\frac{3h^2+4h-10}{h}.}[/tex]