Q. 7 - Calculus

Question

Suppose $f$ is defined and continuous everywhere. Why is testing the sign of the derivative $f$  at just one point sufficient to determine the sign of $f$ on the whole interval between critical points of $f$ ?

Step-by-Step Solution

Answer

Because a function can only change signs at roots and discontinuities or non-domain points. 

Step 1. Given Information.

The function $f$ is defined and continuous everywhere.

Step 2. Testing the sign of f .

Testing the sign of the derivative $f\text{'}$ at just one point is sufficient to determine the sign of $f\text{'}$on the whole interval between critical points of $f$ because a function can only change the sign at roots and discontinuities or non-domain points.