Explanation
given
[tex]f(x)=5x^2-9x+11[/tex]find
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Step 1
a)evaluate the function for (x+h)
so
[tex]\begin{gathered} f(x)=5x^2-9x+11 \\ f(x+h)=5(x+h)^2-9(x+h)+11 \\ expand \\ f(x+h)=5(x^2+2xh+h^2)-9x-9h+11 \\ appply\text{ distributive property} \\ f(x+h)=5x^2+10xh+5h^2-9x-9h+11 \\ f(x+h)=5x^{2}+10xh+5h^{2}-9x-9h+11 \end{gathered}[/tex]b) now replace
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h} \\ \frac{5x^2+10xh+5h^2-9x-9h+11-(5x^2-9x+11)}{h} \\ \frac{5x^2+10xh+5h^2-9x-9h+11-5x^2+9x-11}{h} \\ add\text{ like terms in the numerator} \\ \frac{10xh+5h^2-9h}{h} \\ factorize\text{ h in the numerator} \\ \frac{h(10x+5h^-9)}{h} \\ 10x+5h-9 \end{gathered}[/tex]therefore,rthe answer is
[tex]10x+5h-9[/tex]I hope this helps you this helps you this helps yo this helps y this helps
