Answer:
(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) <em>Find the derivative of the function using the definition of derivative</em>:
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) <em>State the domain of the function and the domain of its derivative</em>:
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: