# What are the critical values, if any, of #f(x) = x^(2/3)+x^(-1/3) #?

##### 1 Answer

Critical value is

#### Explanation:

#f(x)=x^(2/3)+x^(-1/3)#

#f'(x)=(2/3) x^(-1/3)-(1/3)x^(-4/3)#

To find the critical points set

#( 2x^(-1/3)-x^(-4/3))/3=0#

#2x^(-1/3)-x^(-4/3) = 0#

#2x^(-1/3)=x^(-4/3) -># use law of exponential

#2/(x^(1/3))=1/(x^(4/3)) -># cross multiplication

#x^(4/3)/x^(1/3)=1/2#

#x=1/2#