What is the extreme sqrt(-x^2+2x) ?

The extreme sqrt(-x^2+2x) is Minimum(0,0),Maximum(1,1),Minimum(2,0)

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extreme sqrt(-x^2+2x)

extreme points

- x^{2} + 2 x

Minimum (0, 0), Maximum (1, 1), Minimum (2, 0)

Solution steps

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

Find intervals:

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < 2

Plug

x = 0

into

- x^{2} + 2 x : 0

Minimum (0, 0)

Plug

x = 1

into

- x^{2} + 2 x : 1

Maximum (1, 1)

Plug

x = 2

into

- x^{2} + 2 x : 0

Minimum (2, 0)

Minimum (0, 0), Maximum (1, 1), Minimum (2, 0)

f (x) = x y + \frac{50}{x} + \frac{20}{x}

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

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

f (x) = - 2 x^{2} - 3 x + 4

\frac{1}{x ^{3} - 2 x}

What is the extreme sqrt(-x^2+2x) ?
The extreme sqrt(-x^2+2x) is Minimum(0,0),Maximum(1,1),Minimum(2,0)