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

f(x)=12 x^4/3 - 6 x^1/3 ,x belongs to [-1,1].

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

Question

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

Ajanta Trivedi · Accepted Answer

the given function is: $f (x) = 12 x^{4 / 3} - 6 x^{1 / 3} a n d x \in [- 1, 1]$

$f' (x) = 12 * \frac{4}{3} * x^{\frac{4}{3} - 1} - 6 * \frac{1}{3} * x^{\frac{1}{3} - 1} = 16 x^{1 / 3} - 2 x^{- 2 / 3} = 2 x^{- 2 / 3} [8 x - 1] = \frac{2}{x^{2 / 3}} [8 x - 1]$

put $f' (x) = 0 \Rightarrow x = \frac{1}{8}$

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

$f (- 1) = 12 - 6 * (- 1) = 12 + 6 = 18 f (1) = 12 - 6 = 6 f (\frac{1}{8}) = 12 * (\frac{1}{8})^{4 / 3} - 6 * (\frac{1}{8})^{1 / 3} = 12 * \frac{1}{16} - \frac{6}{2} = \frac{3}{4} - 3 = - \frac{9}{4}$

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

and absolute maximum value = 18 at x = -1

hope this helps you.

cheers!!

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.

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

f(x)=12 x^4/3 - 6 x^1/3 ,x belongs to [-1,1].

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