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Popular >

extreme y=x^3-6x^2+9x

Solution

extreme points

y = x^{3} - 6 x^{2} + 9 x

Solution

Maximum (1, 4), Minimum (3, 0)

Solution steps

f^{'} (x) = 3 x^{2} - 12 x + 9

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

x^{3} - 6 x^{2} + 9 x : 4

Maximum (1, 4)

Plug

x = 3

into

x^{3} - 6 x^{2} + 9 x : 0

Minimum (3, 0)

Maximum (1, 4), Minimum (3, 0)

Popular Examples

extreme f(x)=2x^4-16x^2+20x-7 extreme points

f (x) = 2 x^{4} - 16 x^{2} + 20 x - 7

extreme f(x)=4x^3-4x extreme points

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

extreme f(x)=x-6sqrt(x-1)extreme points

f (x) = x - 6 x - 1

extreme f(x,y)=x^3+y^3-15xy extreme points

f (x, y) = x^{3} + y^{3} - 15 x y

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

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

Frequently Asked Questions (FAQ)

What is the extreme y=x^3-6x^2+9x ?
The extreme y=x^3-6x^2+9x is Maximum(1,4),Minimum(3,0)