Question

Find and simplify the difference quotient of the​ form, %7D%20%2C%20h%5Cneq%200" id="TexFormula1" title="\frac{f(x+h)-f(x)}{h} , h\neq 0" alt="\frac{f(x+h)-f(x)}{h} , h\neq 0" align="absmiddle" class="latex-formula">
$f(x)=-10x+9$
$\frac{f(x+h)-f(x)}{h} =$

Answer 1

With $f(x)=-10x+9$, we have

$f(x+h) = -10(x+h) + 9 = -10x + 9 - 10h$

Then the difference quotient is

$\dfrac{f(x+h)-f(x)}h = \dfrac{(-10x+9-10h)-(-10x+9)}h = \dfrac{-10h}h = -10$

since h ≠ 0.