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Find any relative extrema of the function.

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Find any relative extrema of the function.

f (x) = arcsec x - x
asked Feb 2, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The function is .

Rewrite the function, .

Derivative on each side with respect to .

Apply the derivatives of inverse trigonometric function: .

Step 2:

To find the relative extrema, solve .

Squaring on each side.

image

Let image.

image

The above equation is in the form of a quadratic equation image.

The roots of the quadratic equation is image.

Step 3:

Compare image with image.

image

image

Substitute image in above value.

image

image

image

=undefined

Step 4:

image

Use x values to find the maximum and minimum points.

Substitute image in .

image

The maximum point is image.

Substitute image in .

image

The minimum point is image.

Solution :

The relative maximum point is image.

The relative minimum point is image.

answered Feb 2, 2015 by james Pupil

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