What is the extreme f(x)=x*sqrt(x+2) ?

The extreme f(x)=x*sqrt(x+2) is Maximum(-2,0),Minimum(-4/3 ,-(4sqrt(2))/(3sqrt(3)))

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extreme f(x)=x*sqrt(x+2)

extreme points

f (x) = x \cdot x + 2

Maximum (- 2, 0), Minimum (- \frac{4}{3}, - \frac{4 2}{3 3})

Solution steps

f^{'} (x) = \frac{3 x + 4}{2 x + 2}

Find intervals:

Decreasing

: - 2 < x < - \frac{4}{3},

Increasing

: - \frac{4}{3} < x < \infty

Plug

x = - 2

into

x \cdot x + 2 : 0

Maximum (- 2, 0)

Plug

x = - \frac{4}{3}

into

x \cdot x + 2 : - \frac{4 2}{3 3}

Minimum (- \frac{4}{3}, - \frac{4 2}{3 3})

Maximum (- 2, 0), Minimum (- \frac{4}{3}, - \frac{4 2}{3 3})

f (x, y) = 13 - 4 x + 8 y

g (x) = x + \frac{4}{x ^{2}}

f (1, y) = y^{2} + y + 6

f (x) = - 10 x^{2} + 60 x - 80

f (x) = - \frac{5}{x - 2}

What is the extreme f(x)=x*sqrt(x+2) ?
The extreme f(x)=x*sqrt(x+2) is Maximum(-2,0),Minimum(-4/3 ,-(4sqrt(2))/(3sqrt(3)))