Question

find the difference quotient of f, that is, find \\(\frac{f(x + h) - f(x)}{h}\\), \\(h \
eq 0\\), for the following function.\\(f(x) = -8x + 5\\)\\(\frac{f(x + h) - f(x)}{h} = \square\\) (simplify your answer.)

Explanation:

Step1: Compute $f(x+h)$

$f(x+h) = -8(x+h) + 5 = -8x -8h +5$

Step2: Substitute into difference quotient

$\frac{f(x+h)-f(x)}{h} = \frac{(-8x -8h +5) - (-8x +5)}{h}$

Step3: Simplify numerator

$\frac{-8x -8h +5 +8x -5}{h} = \frac{-8h}{h}$

Step4: Cancel common factor $h$

$\frac{-8h}{h} = -8$

Answer:

$-8$