This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Find the derivative of the function using the definition of derivative.
State the domain of the function and the domain of its derivative.
f(x) = 1/10x-1/3

(i) The derivative of the function is .

(ii) The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:

The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:

Step-by-step explanation:

(i) Find the derivative of the function using the definition of derivative:

The derivative is defined by the following limit:

(1)

If we know that , then the definition of derivative is expanded:

The derivative of the function is .

(ii) State the domain of the function and the domain of its derivative:

The domain of all first order polynomials (linear functions) is the set of all real numbers. That is:

The domain of all zero order polynomials (constant functions) is the set of all real numbers. That is:

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step-by-step explanation:

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step-by-step explanation: