Find the derivative of the function using the definition of derivative.f(x) = mx + qf ‘(x) = State the domain of the function. (Enter

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.)

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Arya 3 weeks 2022-01-08T14:33:41+00:00 1 Answer 0 views 0

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    2022-01-08T14:35:17+00:00

    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)

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