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