Q. 6 - Calculus

Question

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

The Intermediate Value Theorem: If f is          on a closed interval$[a,b]$, then for any K strictly between          and         , there exists at least one $c\in (a,b)$such that         . 

Step-by-Step Solution

Answer

 The Intermediate Value Theorem: If f is continuous on a closed interval$[a,b]$, then for any K strictly between $\underline{f\left(a\right)}$and$\underline{f\left(b\right)}$, there exists at least one $c\in (a,b)$such that$\underline{f\left(c\right)=k}$.

Step 1. Given information.

The given incomplete statement is following. 

The Intermediate Value Theorem: If f is        on a closed interval$[a,b]$, then for any K strictly between       and        , there exists at least one $c\in (a,b)$such that          . 

Step 2. Explanation.

The Intermediate Value Theorem: If f is continuous on a closed interval$[a,b]$, then for any K strictly between $\underline{f\left(a\right) }$and $\underline{f\left(b\right)}$, there exists at least one $c\in (a,b)$such that$\underline{f\left(c\right)=k}$.