Q. 18 - Calculus

Question

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold. 

Step-by-Step Solution

Answer

A labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem is

Step 1. Given Information.

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

Step 2. Sketching a graph

The graph is