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Popular >

extreme y=3x-x^3

Solution

extreme points

y = 3 x - x^{3}

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

3 x - x^{3} : - 2

Minimum (- 1, - 2)

Plug

x = 1

into

3 x - x^{3} : 2

Maximum (1, 2)

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

Popular Examples

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f (x, y) = x y - 4 x - 4 y - x^{2} - y^{2}

extreme f(x)=(x^2-4)/(x^2+4),-4<= x<= 4 extreme points

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extreme f(x,y)=y^2+sqrt(x-4)extreme points

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

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

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

extreme f(x)=x^2e^{2x}extreme points

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

Frequently Asked Questions (FAQ)

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