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#
