What is the extreme xsqrt(7-x) ?

The extreme xsqrt(7-x) is Maximum(14/3 ,(14sqrt(7))/(3sqrt(3))),Minimum(7,0)

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extreme xsqrt(7-x)

extreme points

x 7 - x

Maximum (\frac{14}{3}, \frac{14 7}{3 3}), Minimum (7, 0)

Solution steps

f^{'} (x) = \frac{- 3 x + 14}{2 7 - x}

Find intervals:

Increasing

: - \infty < x < \frac{14}{3},

Decreasing

: \frac{14}{3} < x < 7

Plug

x = \frac{14}{3}

into

x 7 - x : \frac{14 7}{3 3}

Maximum (\frac{14}{3}, \frac{14 7}{3 3})

Plug

x = 7

into

x 7 - x : 0

Minimum (7, 0)

Maximum (\frac{14}{3}, \frac{14 7}{3 3}), Minimum (7, 0)

f (x) = 2 cos (2 x) - 2

2 x e^{- x^{2}}

R (x, y) = - 5 x^{2} - 8 y^{2} - 2 x y + 42 x + 102 y

f (x) = ln (x) + x^{2}

4 x^{2} - 4 x

What is the extreme xsqrt(7-x) ?
The extreme xsqrt(7-x) is Maximum(14/3 ,(14sqrt(7))/(3sqrt(3))),Minimum(7,0)