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Popular >

extreme x^4+4x^3

Solution

extreme points

x^{4} + 4 x^{3}

Solution

Minimum (- 3, - 27), Saddle (0, 0)

Solution steps

f^{'} (x) = 4 x^{3} + 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{4} + 4 x^{3} : - 27

Minimum (- 3, - 27)

Plug

x = 0

into

x^{4} + 4 x^{3} : 0

Saddle (0, 0)

Minimum (- 3, - 27), Saddle (0, 0)

Popular Examples

extreme 0.07x^3-1.6x^2+5.13x+5.35 extreme points

0.07 x^{3} - 1.6 x^{2} + 5.13 x + 5.35

extreme f(x)=x^3+3x^2+b extreme points

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

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

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

extreme f(x)=6x^2 extreme points

f (x) = 6 x^{2}

extreme f(x,y)=x^3+y^3+3xy+5 extreme points

f (x, y) = x^{3} + y^{3} + 3 x y + 5

Frequently Asked Questions (FAQ)

What is the extreme x^4+4x^3 ?
The extreme x^4+4x^3 is Minimum(-3,-27),Saddle(0,0)