Q. 5 - Calculus

Question

Fill in the blanks to complete each of the following theorem statements: 

The Extreme Value Theorem: If f is on a closed interval$[a,b]$, then there exist values M and m in the interval$[a,b]$ such that $f\left(M\right)$is        and $f\left(m\right)$is         . 

Step-by-Step Solution

Answer

 The Extreme Value Theorem: If f is on a closed interval$[a,b]$, then there exist values M and m in the interval$[a,b]$ such that $f\left(M\right)$is maximum and $f\left(m\right)$is minimum.

Step 1. Given information.

The given incomplete statement is the following. 

 The Extreme Value Theorem: If f is on a closed interval$[a,b]$, then there exist values M and m in the interval$[a,b]$ such that $f\left(M\right)$is        and $f\left(m\right)$is         . 

Step 2. Explanation.

 The Extreme Value Theorem: If f is on a closed interval$[a,b]$, then there exist values M and m in the interval$[a,b]$ such that $f\left(M\right)$is maximum and $f\left(m\right)$minimum.