### Home > CALC > Chapter 6 > Lesson 6.4.3 > Problem 6-163

6-163.

If is a differentiable function such that

*for all real numbers*

*and if*

*, determine if*

*and*

*are relative minimums or maximums. Justify your answer.*

Determine if is an extrema candidate.

That is, does

*or does*

Yes,

*is an extrema candidate! It could be a relative max, a relative min, or neither.*

Determine if is a relative max, relative min or neither. Use the 1st-derivative test:

To do this, determine if

*changes sign at*

*.*

Evaluate a little to the left and a little to the right.

To the left:

*(some negative value)*

To the right:

*(some negative value)*

Conclusion: Since

*and*

*changes from positive to negative at*

*, therefore*

*is a relative maxima.*

Now test .