What is the extreme f(x)=x+sqrt(3-x) ?

The extreme f(x)=x+sqrt(3-x) is Maximum(11/4 , 13/4),Minimum(3,3)

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extreme f(x)=x+sqrt(3-x)

extreme

Maximum (\frac{11}{4}, \frac{13}{4}), Minimum (3, 3)

Solution steps

f^{'} (x) = 1 - \frac{1}{2 3 - x}

Find intervals:

Increasing

: - \infty < x < \frac{11}{4},

Decreasing

: \frac{11}{4} < x < 3

Plug

x = \frac{11}{4}

into

x + 3 - x : \frac{13}{4}

Maximum (\frac{11}{4}, \frac{13}{4})

Plug

x = 3

into

x + 3 - x : 3

Minimum (3, 3)

Maximum (\frac{11}{4}, \frac{13}{4}), Minimum (3, 3)

What is the extreme f(x)=x+sqrt(3-x) ?
The extreme f(x)=x+sqrt(3-x) is Maximum(11/4 , 13/4),Minimum(3,3)