step 1:
\ The function is .
Apply first derivative with respect to .
To find the relative extrema, by equating .
Apply zero product property
\ and
and
Hence, the critical values of are
and
.
substitute in
.
Hence,
The point is .
Substitute in
.
Hence, .
The point is .
The relative extrema points are and
.
Using second derivative test, determine the relative extrema.
\Apply second derivative with respect to .
.
Point | \![]() | \
![]() | \
Sign of ![]() | \
\
| \
\
| \
Conclusion | \Relative maximum | \Relative minimum | \
\
The relative maximum at .
The relative minimum at .
Solution:
\The relative maximum at .
The relative minimum at .