What is the extreme f(x)=sqrt(x)+sqrt(4-x) ?

The extreme f(x)=sqrt(x)+sqrt(4-x) is Minimum(0,2),Maximum(2,2sqrt(2)),Minimum(4,2)

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extreme f(x)=sqrt(x)+sqrt(4-x)

extreme

Minimum (0, 2), Maximum (2, 22), Minimum (4, 2)

Solution steps

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

Find intervals:

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < 4

Plug

x = 0

into

x + 4 - x : 2

Minimum (0, 2)

Plug

x = 2

into

x + 4 - x : 22

Maximum (2, 22)

Plug

x = 4

into

x + 4 - x : 2

Minimum (4, 2)

Minimum (0, 2), Maximum (2, 22), Minimum (4, 2)

What is the extreme f(x)=sqrt(x)+sqrt(4-x) ?
The extreme f(x)=sqrt(x)+sqrt(4-x) is Minimum(0,2),Maximum(2,2sqrt(2)),Minimum(4,2)