What is the extreme f(x)=(x+2)(-x)^{1/2} ?

The extreme f(x)=(x+2)(-x)^{1/2} is Maximum(-2/3 ,(4*2^{1/2})/(3*3^{1/2)}),Minimum(0,Undefined)

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extreme f(x)=(x+2)(-x)^{1/2}

extreme points

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

Maximum (- \frac{2}{3}, \frac{4 \cdot 2 ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}}), Minimum (0, Undefined)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

: - \frac{2}{3} < x < 0

Plug

x = - \frac{2}{3}

into

(x + 2) (- x)^{\frac{1}{2}} : \frac{4 \cdot 2 ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}}

Maximum (- \frac{2}{3}, \frac{4 \cdot 2 ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}})

Plug

x = 0

into

(x + 2) (- x)^{\frac{1}{2}} :

Undefined

Minimum (0, Undefined)

Maximum (- \frac{2}{3}, \frac{4 \cdot 2 ^{\frac{1}{2}}}{3 \cdot 3 ^{\frac{1}{2}}}), Minimum (0, Undefined)

y = \frac{x}{x ^{2} + 1}

(38.7, 38.24), (84.6, 87.04)

(- 1, 6), (- 6, - 1)

f (x) = 0.2 x^{2}

(- 2, 0), (0, 3)

What is the extreme f(x)=(x+2)(-x)^{1/2} ?
The extreme f(x)=(x+2)(-x)^{1/2} is Maximum(-2/3 ,(4*2^{1/2})/(3*3^{1/2)}),Minimum(0,Undefined)