Question

Find the absolute extrema if they​ exist, as well as all values of x where they​ occur, for the function:

f(x) = 2x^3 - 48 ln x ; on the domain [ 1 , 5 ]

Answer 1

Given, C P(x) = 2x - 48 lox l'a) = 6x² - 48 X . : f'(x) = 0 >> 6x?– 48 = 0 albo H. 2 = 2 P"64) = 12.2 + young p" (a) at a= 2 = 24 + 48 - 24 + 12 = 3670 : at q=2, f w) has minima. : extrema = 2(2)% -48 log(2) = 2x8 – 48(0.6991) -11.2688 absolute extrema - 17. 2688