We need to calculate the expression for f(x+h) before we can find the difference quotioent.
[tex]\begin{gathered} f(x+h)=5\cdot(x+h)^2+1 \\ f(x+h)=5x^2+10hx+5h^2+1 \end{gathered}[/tex]
Now we can replace the value of f(x+h) and the value of f(x) on the expression, and simplify it as much as possible to determine the quotient.
[tex]\begin{gathered} \frac{5x^2+10hx+5h^2+1-5x^2-1}{h} \\ \frac{10hx+5h^2}{h} \\ \frac{h(10x+5h)}{h} \\ 10x+5h \end{gathered}[/tex]
The value of the quotient is "10x + 5h"
