Question

The polynomial function is an odd function. If x = c is a relative maximum of f(x), which of the following statements about f(-c) must be true?

a. f(-c) is also a relative maximum.
b. f(-c) is a relative minimum.
c. f(-c) is also a relative minimum.
d. f(-c) is neither a maximum nor a minimum.

Answer 1

If x = c is a relative maximum of an odd function, f(-c) is also a relative maximum.

Step-by-step explanation:

An odd function has the property that f(x) = -f(-x). If x = c is a relative maximum of the polynomial function f(x), then we know that f(c) is greater than or equal to f(x) for every x in the domain of the function. To determine the statement about f(-c), we need to substitute -c into the function and compare it to f(c). If f(-c) is also a relative maximum, then it would mean that f(c) is greater than or equal to f(-c), which matches the definition of an odd function. Therefore, the correct statement is a. f(-c) is also a relative maximum.