Question

Concepts and Vocabulary

True or False: A function f has a local maximum at c if there is an open interval I containing c so that for all x in I, $f\left(x\right)\le f\left(c\right)$

Short answer

True

Step-by-step solution

Given Information 

A function f has a local maximum at c if there is an open interval I containing c so that for all x in I, $f\left(x\right)\le f\left(c\right)$

local maximum or minimum 

If the value of f at c is less than or equal to the values of f on I, then f has a local

minimum at c.

If the value of f at c is greater than or equal to the values of f on I, then f has a local

maximum at c.

A function f has a local maximum at c if there is an open interval I containing c so that for all x in I, $f\left(x\right)\le f\left(c\right)$. We call f(c) a local maximum value of f. Given statement is true.