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

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

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

extreme points

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

Maximum (- 2, 2), Minimum (0, - 2)

Solution steps

f^{'} (x) = 3 x^{2} + 6 x

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 2)

Plug

x = 0

into

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

Minimum (0, - 2)

Maximum (- 2, 2), Minimum (0, - 2)

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

f (x) = x^{3} - 6 x y + 8 y^{3}

f (x) = \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x

f (x, y) = 5 x y - 7 x^{2} + 3 x - 6 y + 2

f (x) = \frac{x ^{2} - 16}{x ^{2} + 16}

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