Question

Which of the following functions has neither a local nor global extreme value? Explain.

(A) () = √
(B) () = 2
(C) () = 3
( D) () = 4

Answer 1

A function has neither a local nor global extreme value if it is a constant function or a function without any restricted domain or range.

Step-by-step explanation:

A function has a local extreme value if there is a point in its domain where the function reaches a maximum or minimum. A function has a global extreme value if it reaches a maximum or minimum over its entire domain.

For the given options:

• (A) () = √: This function has neither a local nor global extreme value because it is a non-constant function and does not have any restricted domain or range.
• (B) () = 2: This function is a constant function, meaning it has the same output value (2) for every input value. Since it is constant, it does not have any maximum or minimum values either locally or globally.
• (C) () = 3: This function is also a constant function with an output value of 3 for every input value. Like the previous function, it does not have any local or global extreme values.
• (D) () = 4: This function is again a constant function. It has an output value of 4 for every input value, so it does not have any local or global extreme values.

Therefore, options (A), (B), (C), and (D) do not have any local or global extreme values.