Q. 7 - Calculus

Question

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

A function f can change sign from positive to negative, or vice versa, at$x=c$ only if $f\left(x\right)$is         ,         , or         at$x=c$.

Step-by-Step Solution

Answer

 A function f can change sign from positive to negative, or vice versa, at$x=c$ only if $f\left(x\right)$is zero, undefined, or discontinuous at $x=c.$

Step 1. Given information.

The given incomplete statement is folowing. 

A function f can change sign from positive to negative, or vice versa, at$x=c$ only if $f\left(x\right)$is        ,        , or          at$x=c$.

Step 2. Explanation.

A function f can change sign from positive to negative, or vice versa, at$x=c$ only if $f\left(x\right)$is zero, undefined, or discontinuous at $x=c.$