What is the extreme f(x)=x+sqrt(7-x) ?

The extreme f(x)=x+sqrt(7-x) is Maximum(27/4 , 29/4),Minimum(7,7)

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extreme f(x)=x+sqrt(7-x)

extreme points

f (x) = x + 7 - x

Maximum (\frac{27}{4}, \frac{29}{4}), Minimum (7, 7)

Solution steps

f^{'} (x) = 1 - \frac{1}{2 7 - x}

Find intervals:

Increasing

: - \infty < x < \frac{27}{4},

Decreasing

: \frac{27}{4} < x < 7

Plug

x = \frac{27}{4}

into

x + 7 - x : \frac{29}{4}

Maximum (\frac{27}{4}, \frac{29}{4})

Plug

x = 7

into

x + 7 - x : 7

Minimum (7, 7)

Maximum (\frac{27}{4}, \frac{29}{4}), Minimum (7, 7)

f (x) = x^{3} + 2 x^{2} - 3 x

- 5 x^{3} + 2 x^{2} - x + 20

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

P (a, b) = a^{2} - 6 a + 9 - b^{2}

f (x, y) = x^{3} + y^{3} + 15 x y

What is the extreme f(x)=x+sqrt(7-x) ?
The extreme f(x)=x+sqrt(7-x) is Maximum(27/4 , 29/4),Minimum(7,7)