State whether the following statement is true or false. A function f has a local maximum at c if there is an open interval I containing c such that for all x in I, .
Choose the correct answer below.
A.
True, because if f has a local maximum at c, then the value of f at c is greater than or equal to the values of f near c.
B.
False, because if f has a local maximum at c, then the value of f at c is the smallest value of f in the domain.
C.
True, because if f has a local maximum at c, then the value of f at c is the largest value of f in the domain.
D.
False, because if f has a local maximum at c, then the value of f at c is less than or equal to the values of f near c.