What is the extreme f(x)=x+sqrt(8-x) ?

The extreme f(x)=x+sqrt(8-x) is Maximum(31/4 , 33/4),Minimum(8,8)

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extreme f(x)=x+sqrt(8-x)

extreme

Maximum (\frac{31}{4}, \frac{33}{4}), Minimum (8, 8)

Solution steps

f^{'} (x) = 1 - \frac{1}{2 8 - x}

Find intervals:

Increasing

: - \infty < x < \frac{31}{4},

Decreasing

: \frac{31}{4} < x < 8

Plug

x = \frac{31}{4}

into

x + 8 - x : \frac{33}{4}

Maximum (\frac{31}{4}, \frac{33}{4})

Plug

x = 8

into

x + 8 - x : 8

Minimum (8, 8)

Maximum (\frac{31}{4}, \frac{33}{4}), Minimum (8, 8)

What is the extreme f(x)=x+sqrt(8-x) ?
The extreme f(x)=x+sqrt(8-x) is Maximum(31/4 , 33/4),Minimum(8,8)