What is the extreme f(x)=2x^2+x^3 ?

The extreme f(x)=2x^2+x^3 is Maximum(-4/3 , 32/27),Minimum(0,0)

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extreme f(x)=2x^2+x^3

extreme points

f (x) = 2 x^{2} + x^{3}

Maximum (- \frac{4}{3}, \frac{32}{27}), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

: - \frac{4}{3} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{4}{3}

into

2 x^{2} + x^{3} : \frac{32}{27}

Maximum (- \frac{4}{3}, \frac{32}{27})

Plug

x = 0

into

2 x^{2} + x^{3} : 0

Minimum (0, 0)

Maximum (- \frac{4}{3}, \frac{32}{27}), Minimum (0, 0)

f (x) = - 6 cos (x - 2 π)

f (x, y) = x^{2} + y^{2} - 3

x^{2} - x - ln (x)

x^{2} + \frac{8}{x}

f (x) = 3 x_{2} + 4 x - 2

What is the extreme f(x)=2x^2+x^3 ?
The extreme f(x)=2x^2+x^3 is Maximum(-4/3 , 32/27),Minimum(0,0)