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Popular >

extreme x^3-12x^2+36x

Solution

extreme points

x^{3} - 12 x^{2} + 36 x

Solution

Maximum (2, 32), Minimum (6, 0)

Solution steps

f^{'} (x) = 3 x^{2} - 24 x + 36

Find intervals:

Increasing

: - \infty < x < 2,

Decreasing

: 2 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = 2

into

x^{3} - 12 x^{2} + 36 x : 32

Maximum (2, 32)

Plug

x = 6

into

x^{3} - 12 x^{2} + 36 x : 0

Minimum (6, 0)

Maximum (2, 32), Minimum (6, 0)

Popular Examples

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extreme x^3-12x+2 extreme points

x^{3} - 12 x + 2

extreme f(x,y)= 1/3 y^3+x^2-2xy-15y+12 extreme points

f (x, y) = \frac{1}{3} y^{3} + x^{2} - 2 x y - 15 y + 12

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extreme F(x,y)=y^3+3x^2y-6x^2-6y^2+2 extreme points

F (x, y) = y^{3} + 3 x^{2} y - 6 x^{2} - 6 y^{2} + 2

Frequently Asked Questions (FAQ)

What is the extreme x^3-12x^2+36x ?
The extreme x^3-12x^2+36x is Maximum(2,32),Minimum(6,0)