What is the extreme f(x)=-3xsqrt(x+1) ?

The extreme f(x)=-3xsqrt(x+1) is Minimum(-1,0),Maximum(-2/3 ,2sqrt(1/3))

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extreme f(x)=-3xsqrt(x+1)

extreme points

f (x) = - 3 x x + 1

Minimum (- 1, 0), Maximum (- \frac{2}{3}, 2 \frac{1}{3})

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Plug

x = - 1

into

- 3 x x + 1 : 0

Minimum (- 1, 0)

Plug

x = - \frac{2}{3}

into

- 3 x x + 1 : 2 \frac{1}{3}

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

Minimum (- 1, 0), Maximum (- \frac{2}{3}, 2 \frac{1}{3})

f (x) = - 20 x^{6} - 5 x^{3} + x^{2} - 17

f (x) = \frac{π r ^{2}}{2} + \frac{( 76 - π x - x )}{2} \cdot x

10 x^{2} y - 5 x^{2} - 4 y^{2} - x^{4} - 2 y^{4}

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

36 - x^{2} - x + 3

What is the extreme f(x)=-3xsqrt(x+1) ?
The extreme f(x)=-3xsqrt(x+1) is Minimum(-1,0),Maximum(-2/3 ,2sqrt(1/3))