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

The extreme f(x)=3+3x^2-2x^3 is Minimum(0,3),Maximum(1,4)

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

extreme points

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

Minimum (0, 3), Maximum (1, 4)

Solution steps

f^{'} (x) = - 6 x^{2} + 6 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 0

into

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

Minimum (0, 3)

Plug

x = 1

into

3 + 3 x^{2} - 2 x^{3} : 4

Maximum (1, 4)

Minimum (0, 3), Maximum (1, 4)

f (x) = x^{4} - 72 x + 5

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

f (x, y) = (x - y) (2 x + y) (x + 1)

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

2 x^{2} + 9

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