Question

Find any relative extrema of the function.

f (x) = arcsec x - x

Answer 1

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.

Let .

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

The roots of the quadratic equation is .

Step 3:

Compare with .

Substitute in above value.

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Step 4:

Use x values to find the maximum and minimum points.

Substitute in .

The maximum point is .

Substitute in .

The minimum point is .

Solution :

The relative maximum point is .

The relative minimum point is .