What is the extreme f(x,y)=x^3-3x ?

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

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extreme f(x,y)=x^3-3x

extreme points

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

Maximum (- 1, 2), Minimum (1, - 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{3} - 3 x : 2

Maximum (- 1, 2)

Plug

x = 1

into

x^{3} - 3 x : - 2

Minimum (1, - 2)

Maximum (- 1, 2), Minimum (1, - 2)

f (x) = 2 x^{2} + 3, - 1 \leq x \leq 2

f (x) = sin (π x) (- \frac{1}{3}, \frac{1}{3})

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

f (x, y) = 3 x^{2} - 6 x + 4 y^{2} + 8

f (x) = 2 x^{3} + 11 x^{2} - 8 x - 12

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