en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme-x^3+3x^2-1

Solution

extreme points

- x^{3} + 3 x^{2} - 1

Solution

Minimum (0, - 1), Maximum (2, 3)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

- x^{3} + 3 x^{2} - 1 : - 1

Minimum (0, - 1)

Plug

x = 2

into

- x^{3} + 3 x^{2} - 1 : 3

Maximum (2, 3)

Minimum (0, - 1), Maximum (2, 3)

Popular Examples

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

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

extreme f(x)=(2x)/(x^2-16)extreme points

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

extreme f(x)=x^{2/3}(x-1)extreme points

f (x) = x^{\frac{2}{3}} (x - 1)

extreme x/((x+1)^2)extreme points

\frac{x}{( x + 1 ) ^{2}}

extreme f(x)=-x^4+8x^3-18x^2 extreme points

f (x) = - x^{4} + 8 x^{3} - 18 x^{2}

Frequently Asked Questions (FAQ)

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