What is the extreme y=x+sqrt(1-x) ?

The extreme y=x+sqrt(1-x) is Maximum(3/4 , 5/4),Minimum(1,1)

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extreme y=x+sqrt(1-x)

extreme points

y = x + 1 - x

Maximum (\frac{3}{4}, \frac{5}{4}), Minimum (1, 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < 1

Plug

x = \frac{3}{4}

into

x + 1 - x : \frac{5}{4}

Maximum (\frac{3}{4}, \frac{5}{4})

Plug

x = 1

into

x + 1 - x : 1

Minimum (1, 1)

Maximum (\frac{3}{4}, \frac{5}{4}), Minimum (1, 1)

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

e^{5 x} + e^{- x}

2 (x^{2} + y^{2}) e^{y^{2} - x^{2}}

f (x, y) = 2 x^{3} - 3 x^{2} y - 12 x^{2} - 3 y^{2}

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

What is the extreme y=x+sqrt(1-x) ?
The extreme y=x+sqrt(1-x) is Maximum(3/4 , 5/4),Minimum(1,1)