What is the extreme f(x)=x-sqrt(x) ?

The extreme f(x)=x-sqrt(x) is Maximum(0,0),Minimum(1/4 ,-1/4)

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extreme f(x)=x-sqrt(x)

extreme points

f (x) = x - x

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

Solution steps

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

Find intervals:

Decreasing

: 0 < x < \frac{1}{4},

Increasing

: \frac{1}{4} < x < \infty

Plug

x = 0

into

x - x : 0

Maximum (0, 0)

Plug

x = \frac{1}{4}

into

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

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

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

What is the extreme f(x)=x-sqrt(x) ?
The extreme f(x)=x-sqrt(x) is Maximum(0,0),Minimum(1/4 ,-1/4)