Question

fill in the blanks. the expression $\frac{f(x + h)-f(x)}{h}$, $h
eq0$, is called the of the function f. we find this expression by replacing x with each time x appears in the functions equation. then we subtract. after simplifying, we factor from the numerator and divide out identical factors of in the numerator and denominator.

Explanation:

The expression $\frac{f(x + h)-f(x)}{h}, h
eq0$ is the difference - quotient in calculus. To find it, we replace $x$ with $x + h$ in the function's equation, subtract $f(x)$, factor out $h$ from the numerator and cancel out the $h$ terms.

Answer:

The expression $\frac{f(x + h)-f(x)}{h}, h
eq0$, is called the difference - quotient of the function $f$. We find this expression by replacing $x$ with $x + h$ each time $x$ appears in the function's equation. Then we subtract $f(x)$. After simplifying, we factor $h$ from the numerator and divide out identical factors of $h$ in the numerator and denominator.