Question

given the following function, determine the difference quotient, \\(\frac{f(x + h) - f(x)}{h}\\).
\\(f(x) = -2x - 5\\)
answer

Explanation:

Step1: Find $f(x+h)$

Substitute $x+h$ into $f(x)$:
$f(x+h) = -2(x+h) - 5 = -2x - 2h - 5$

Step2: Compute $f(x+h)-f(x)$

Subtract $f(x)$ from $f(x+h)$:
$f(x+h)-f(x) = (-2x - 2h - 5) - (-2x - 5) = -2h$

Step3: Divide by $h$

Calculate the difference quotient:
$\frac{f(x+h)-f(x)}{h} = \frac{-2h}{h}$

Step4: Simplify the expression

Cancel out $h$ (where $h
eq 0$):
$\frac{-2h}{h} = -2$

Answer:

$-2$