### Home > APCALC > Chapter 6 > Lesson 6.4.3 > Problem 6-156

6-156.

Let * *be a differentiable function such that

*for all*

*and*

*. Determine if*

*and*

*are relative extrema. Justify your answer.*

Determine if is an extrema candidate.

That is, does

*or does*

*DNE*

*(some negative value)*

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