Question

problem. 1 : find the derivative of the function using the definition of the derivative.
$f(x) = -6x - 9$
$f(x) = -6$
problem. 1.1 : state the domain of the function. (enter your answer using interval notation.)
$\left( -\infty, \infty \
ight)$
problem. 1.1.1 : state the domain of its derivative. (enter your answer using interval notation.)
$\left( \square, \square \
ight)$

Explanation:

Step1: Analyze the derivative function

The derivative of \( f(x) = -6x - 9 \) is \( f'(x) = -6 \), which is a constant function.

Step2: Determine the domain of a constant function

A constant function (like \( f'(x) = -6 \)) is defined for all real numbers. In interval notation, the set of all real numbers is \( (-\infty, \infty) \).

Answer:

\((-\infty, \infty)\)