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 points

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

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})

f (x) = ln (3 x + 1)

f (x) = - 2 + 5 sin (\frac{π}{12} (x - 2))

f (x) = (2 x - x^{2}) (2 y - y^{2})

f (x, y) = 9 - 2 x + 8 y - x^{2} - 4 y^{2}

f (x) = - 4 x^{5} ln (2 x)

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)