The function is .
Differentiate on each side with respect to .
Derivative of a inverse trigonometric function:
Derivative of a inverse trigonometric function: .
To find the relative extrema,solve .
Squaring on each sides.
\Let .
The above equation is in the form of a quadratic equation
The roots of the quadratic equation is .
Compare with
.
Substitute in above value.
.
The negative root is not considered since, can not be negative.
.
Substitute in
.
The point is .
Substitute in
.
The point is .
Derivative on each side with respect to .
Identify the nature of the extrema points.
\Point | \Sign of ![]() | \
Conclusion | \
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Relative minimum | \
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Relative maximum | \
The relative maximum point is .
The relative minimum point is .
The relative maximum point is .
The relative minimum point is .