What is the extreme 10x^{1/2}-x[100] ?

The extreme 10x^{1/2}-x[100] is Maximum(0,0),Minimum(1/400 , 1/4)

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extreme 10x^{1/2}-x[100]

extreme points

10 x^{\frac{1}{2}} - x [100]

Maximum (0, 0), Minimum (\frac{1}{400}, \frac{1}{4})

Solution steps

f^{'} (x) = \frac{5}{x ^{\frac{1}{2}}} - 100

Find intervals:

Decreasing

: 0 \leq x < 400,

Increasing

: 400 < x < \infty

Plug

x = 0

into

10 x^{\frac{1}{2}} - x [100] : 0

Maximum (0, 0)

Plug

x = \frac{1}{400}

into

10 x^{\frac{1}{2}} - x [100] : \frac{1}{4}

Minimum (\frac{1}{400}, \frac{1}{4})

Maximum (0, 0), Minimum (\frac{1}{400}, \frac{1}{4})

f (x) = 2 x^{3} - 2 x^{2} - 2 x + 6

f (x) = (4 x^{2} - 64)^{\frac{1}{5}}

f (x, y) = e^{y^{2} + x^{3} - 6 x y - 6 x + 2 y}

\frac{2 x + 4}{x ^{2} - 16}

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

What is the extreme 10x^{1/2}-x[100] ?
The extreme 10x^{1/2}-x[100] is Maximum(0,0),Minimum(1/400 , 1/4)