Q. 9 - Precalculus Enhanced with Graphing Utilities

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,  $f\left(x\right)\le f\left(c\right)$

Step-by-Step Solution

Answer

True 

Step 1: 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,  $f\left(x\right)\le f\left(c\right)$

Step 2: 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.