What is the extreme f(x)= 1/2 x^{2/3}-x^{1/3}+3 ?

The extreme f(x)= 1/2 x^{2/3}-x^{1/3}+3 is Minimum(1, 5/2)

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extreme f(x)= 1/2 x^{2/3}-x^{1/3}+3

extreme

Minimum (1, \frac{5}{2})

Solution steps

f^{'} (x) = \frac{1}{3 x ^{\frac{1}{3}}} - \frac{1}{3 x ^{\frac{2}{3}}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

\frac{1}{2} x^{\frac{2}{3}} - x^{\frac{1}{3}} + 3 : \frac{5}{2}

Minimum (1, \frac{5}{2})

What is the extreme f(x)= 1/2 x^{2/3}-x^{1/3}+3 ?
The extreme f(x)= 1/2 x^{2/3}-x^{1/3}+3 is Minimum(1, 5/2)