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

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

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extreme f(x)=x+sqrt(1-x)

extreme points

f (x) = 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)

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