Question

Find the derivative of the function using the definition of derivative.f(x) = mx + qf '(x) =

Answer 1

Answer:

a) $f'(x) = m$

b) $x \in (-\infty, \infty)$

c) $x \in (-\infty, \infty)$

Step-by-step explanation:

We are given the following in the question:

$f(x) = mx + q$

a) We have to find the derivative of the given function.

$f'(x) = \dfrac{f(x+h)-f(x)}{h}\\\\= \dfrac{m(x+h)+q - mx - q}{h}\\\\f'(x) = \dfrac{mh}{h}\\\\f'(x) = m$

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.

$x \in (-\infty, \infty)$

c) Domain of f'(x)

Domain of f'(x) is all real numbers.

$x \in (-\infty, \infty)$