Question

Find any relative extrema of the function. (Round your answers to three decimal places.)

f(x) = arcsec(x) − 8x

relative maximum (x, y)=
relative minimum (x, y) =

Can someone please help me with this question?

Answer 1

(x) = arcsec(x) − 8x

f'(x) = d/dx( arcsec(x) − 8x )

 1/xsqrt( x^2 - 1) - 8

f'(x) = 0

1/xsqrt( x^2 - 1) - 8 = 0

8 x sqrt (x^2-1) = 1

 ( 8 x sqrt (x^2-1) )^2 = 1

64 x^2 ( x^2 - 1) = 1

64 x^4 - 64 x^2 =1

64 x^4 - 64 x^2 - 1 = 0

x = 1.00766 , - 1.00766

 x =   - 1.00766

f(- 1.00766) = arcsec(- 1.00766) − 8( - 1.00766)

f( - 1.00766 ) = 11.07949

x = 1.00766

f(1.00766) = arcsec(1.00766) − 8( 1.00766)

f(1.00766 ) = -7.93790

relative maximum (x, y) = (- 1.00766 , 11.07949 ) relative minimum (x, y) = ( 1.00766 , -7.93790  )