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Popular Functions >

extreme y=x^3-12x

Solution

extreme points

y = x^{3} - 12 x

Solution

Maximum (- 2, 16), Minimum (2, - 16)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

x^{3} - 12 x : 16

Maximum (- 2, 16)

Plug

x = 2

into

x^{3} - 12 x : - 16

Minimum (2, - 16)

Maximum (- 2, 16), Minimum (2, - 16)

Graph

Popular Examples

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

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

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

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

extreme f(x)=x^3-3x^2-1 extreme points

f (x) = x^{3} - 3 x^{2} - 1

extreme f(x)= 1/(x^2-x-6)extreme points

f (x) = \frac{1}{x ^{2} - x - 6}

extreme f(x)=x^3-3/2 x^2-36x-5 extreme points

f (x) = x^{3} - \frac{3}{2} x^{2} - 36 x - 5

Frequently Asked Questions (FAQ)

What is the extreme y=x^3-12x ?
The extreme y=x^3-12x is Maximum(-2,16),Minimum(2,-16)