What are the critical values, if any, of f(x)= x^(3/4) - 2x^(1/4)?

1 Answer
Feb 14, 2016

By the definition I am accustomed to, they are 0 and 4/9.

Explanation:

A critical value of f is a value in the domain of f at which f' does not exists or f'(x) is 0.

The domain of the function f(x)=x^(3/4)-2x^(1/4) is [0,oo).

The derivative is f'(x) =3/4x^(-1/4)-1/2x^(-3/4) = (3x^(1/2)-2)/(4x^(3/2))

f' fails to exist at x=0 and f'(x) = 0 at x=4/9.

Both 0 and 4/9 are in the domain, so both are critical values.