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Popular >

extreme y=x^4-4x^3

Solution

extreme points

y = x^{4} - 4 x^{3}

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

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

Saddle (0, 0)

Plug

x = 3

into

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

Minimum (3, - 27)

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

Popular Examples

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

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

extreme x^3-3x^2 extreme points

x^{3} - 3 x^{2}

extreme f(x,y)=sqrt(|xy|)extreme points

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extreme f(x)=(x^2-8)/(x-3)extreme points

f (x) = \frac{x ^{2} - 8}{x - 3}

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

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

Frequently Asked Questions (FAQ)

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