What is the extreme f(x)=sqrt(x)-\sqrt[4]{x} ?

The extreme f(x)=sqrt(x)-\sqrt[4]{x} is Maximum(0,0),Minimum(1/16 ,-1/4)

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extreme f(x)=sqrt(x)-\sqrt[4]{x}

extreme

Maximum (0, 0), Minimum (\frac{1}{16}, - \frac{1}{4})

Solution steps

f^{'} (x) = \frac{1}{2 x} - \frac{1}{4 x ^{\frac{3}{4}}}

Find intervals:

Decreasing

: 0 < x < \frac{1}{16},

Increasing

: \frac{1}{16} < x < \infty

Plug

x = 0

into

x - 4 x : 0

Maximum (0, 0)

Plug

x = \frac{1}{16}

into

x - 4 x : - \frac{1}{4}

Minimum (\frac{1}{16}, - \frac{1}{4})

Maximum (0, 0), Minimum (\frac{1}{16}, - \frac{1}{4})

What is the extreme f(x)=sqrt(x)-\sqrt[4]{x} ?
The extreme f(x)=sqrt(x)-\sqrt[4]{x} is Maximum(0,0),Minimum(1/16 ,-1/4)