What is the extreme f(x)=3x-2x^2-4/3 x^3 ?

The extreme f(x)=3x-2x^2-4/3 x^3 is Minimum(-3/2 ,-9/2),Maximum(1/2 , 5/6)

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extreme f(x)=3x-2x^2-4/3 x^3

extreme points

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

Minimum (- \frac{3}{2}, - \frac{9}{2}), Maximum (\frac{1}{2}, \frac{5}{6})

Solution steps

f^{'} (x) = 3 - 4 x - 4 x^{2}

Find intervals:

Decreasing

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

Increasing

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

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{3}{2}

into

3 x - 2 x^{2} - \frac{4}{3} x^{3} : - \frac{9}{2}

Minimum (- \frac{3}{2}, - \frac{9}{2})

Plug

x = \frac{1}{2}

into

3 x - 2 x^{2} - \frac{4}{3} x^{3} : \frac{5}{6}

Maximum (\frac{1}{2}, \frac{5}{6})

Minimum (- \frac{3}{2}, - \frac{9}{2}), Maximum (\frac{1}{2}, \frac{5}{6})

f (x) = (x^{3} - 5 x^{2} + 11 x - 11) e^{x}

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

f (x, y) = - 14 + 5 \cdot x^{2} + x \cdot y + y^{2}

f (x) = 5 x + \frac{3}{x}

f (x y) = x y e^{- x^{2} - y^{2}}

What is the extreme f(x)=3x-2x^2-4/3 x^3 ?
The extreme f(x)=3x-2x^2-4/3 x^3 is Minimum(-3/2 ,-9/2),Maximum(1/2 , 5/6)