Question

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

State the domain of the function. (Enter your answer using interval notation.)
State the domain of its derivative. (Enter your answer using interval notation.)

Answer 1

a)
`f'(x) = m`

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

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

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) = (f(x+h)-f(x))/(h)\\\\= (m(x+h)+q - mx - q)/(h)\\\\f'(x) = (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)`