Question

find and simplify the difference quotient \\(\frac{f(x + h) - f(x)}{h}\\), \\(h \
eq 0\\) for the given function \\(f(x) = -7x\\) \\(\frac{f(x + h) - f(x)}{h} = \square\\) (simplify your answer)

Explanation:

Step1: Find $f(x+h)$

$f(x+h) = -7(x+h) = -7x -7h$

Step2: Substitute into difference quotient

$\frac{f(x+h)-f(x)}{h} = \frac{(-7x -7h) - (-7x)}{h}$

Step3: Simplify numerator

$\frac{-7x -7h +7x}{h} = \frac{-7h}{h}$

Step4: Cancel common factor $h$

$\frac{-7h}{h} = -7$

Answer:

$-7$