Answer:
a) [tex]f'(x) = m[/tex]
b) [tex]x \in (-\infty, \infty)[/tex]
c) [tex]x \in (-\infty, \infty)[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]f(x) = mx + q[/tex]
a) We have to find the derivative of the given function.
[tex]f'(x) = \dfrac{f(x+h)-f(x)}{h}\\\\= \dfrac{m(x+h)+q - mx - q}{h}\\\\f'(x) = \dfrac{mh}{h}\\\\f'(x) = m[/tex]
b) Domain of f(x)
Domain is the collection of all values of x for which the function is defined.
Domain of f(x) is all real numbers.
[tex]x \in (-\infty, \infty)[/tex]
c) Domain of f'(x)
Domain of f'(x) is all real numbers.
[tex]x \in (-\infty, \infty)[/tex]
