Summarize the pertinend informalion obiained by applying the graptiny stralegy and sketch the graph of .

Solect the cortect choico beiow and, it necessary, fill in the answer box to completo your choice.
A. The funcion is decreasing on the subinterval(s)
(Type your answor in interval nctation. Type an exacl answer, us ng radicals as nenfed IJse a comma to separale answers as nceded.)
B. The function I is never docreasing.

Select the correct choice below and, if necessary, fill in the answer box to complele your choice.
A. Tho function has a local maximum at .
(Type an exact answeI, using rachads as needed. Uso a comma to separalo answers as needed.)
B. The function I has no focal maximum.

Select the corroct choice below and, if necessary, fill in the answer box to complele your choice.
A. The function has a local minimum at
(Type an exact answet, using radicals as noeded. Use a comma lo separeto answors as noodod.)
B. The function I has no local minimum,

Step 1. Find the Critical Points

Step 2. Monotonicity

• Interval :
  Take . Then,
  So is increasing.
• Interval :
  Take . Then,
  So is decreasing.
• Interval :
  Take . Then,
  So is increasing.
• Interval :
  Take . Then,
  So is decreasing.

Step 3. Local Extrema

• Local Maxima:
  At :
  changes from increasing to decreasing.
  At :
  changes from increasing to decreasing.
  These are local maxima.
• Local Minimum:
  At :
  changes from decreasing (for to ) to increasing (for to ).
  Thus, there is a local minimum at .

Step 4. Summary of Answers

1. Decreasing Intervals:
   The function is decreasing on
2. Local Maximum:
   The function has a local maximum at
3. Local Minimum:
   The function has a local minimum at

Graph Sketch

• The graph is symmetric (even function) because .
• It increases on then decreases on , has a local minimum at , increases on , and finally decreases on .
• The local maxima occur at and ; the local minimum occurs at .

Final Answers

• Choice for the decreasing intervals:
  A. The function is decreasing on .
• Choice for the local maximum:
  A. The function has a local maximum at .
• Choice for the local minimum:
  A. The function has a local minimum at .