Q. 20 - Calculus

Question

Explain why the Intermediate Value Theorem allows us to say that a function can change sign only at discontinuities and zeroes. 

Step-by-Step Solution

Answer

We can show by the graph that a function can change signs only at discontinuities and zeroes. 

The graphs are

and

Step 1. Given Information.

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

Step 2. Explaining.

We can show by the graph that a function can change signs only at discontinuities and zeroes.  

The graphs are

and