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Popular >

extreme y=x(x-4)^3

Solution

extreme points

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

Solution

Minimum (1, - 27), Saddle (4, 0)

Solution steps

f^{'} (x) = 4 (x - 4)^{2} (x - 1)

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 1

into

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

Minimum (1, - 27)

Plug

x = 4

into

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

Saddle (4, 0)

Minimum (1, - 27), Saddle (4, 0)

Popular Examples

extreme f(x,y)=x^4+6sqrt(y-10)extreme points

f (x, y) = x^{4} + 6 y - 10

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

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extreme f(x)=(5x)/(x^2-4)extreme points

f (x) = \frac{5 x}{x ^{2} - 4}

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

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

extreme f(x,y)=2x^2-8x+y^2+16y+100 extreme points

f (x, y) = 2 x^{2} - 8 x + y^{2} + 16 y + 100

Frequently Asked Questions (FAQ)

What is the extreme y=x(x-4)^3 ?
The extreme y=x(x-4)^3 is Minimum(1,-27),Saddle(4,0)