Find absolute maximum and minimum values of a function f given by

f(x)=12 x4/3 - 6 x1/3 ,x belongs to [-1,1].

Ans=absolute maximum value=18 and minimum value of f is -9/4.

the given function is:

put

now we will find the values of f(x) at critical points and at extreme values:

thus absolute minimum value = -9/4 at x = 1/8

and absolute maximum value = 18 at x = -1

hope this helps you.

cheers!!

  • 3

f(X) = 12 x 4/3 - 6x 1/ 3 x belons to [-1,1]

f'(X) = 16 x 1/3 - 2x -2/3

= 2(8x-1) / x 2/3 = 0

:- x = 1/8

f(-1)= 12 + 6 = 8

f(1/8) = - 9/ 4

f(1) = 6

absolute maximum = 18 at x = -1

absolute minimum = -9/4 at x = 1/8

cheeirs

by naresh

  • 3
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