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Popular Functions >

extreme (1-x^2)^2

Solution

extreme points

(1 - x^{2})^{2}

Solution

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

(1 - x^{2})^{2} : 0

Minimum (- 1, 0)

Plug

x = 0

into

(1 - x^{2})^{2} : 1

Maximum (0, 1)

Plug

x = 1

into

(1 - x^{2})^{2} : 0

Minimum (1, 0)

Minimum (- 1, 0), Maximum (0, 1), Minimum (1, 0)

Graph

Popular Examples

extreme f(x)=-10/3 x^3-19x^2-24x+50

extreme y=4cos(x/2)+2

extreme K(r,s)=5r-s

extreme f(x)=20x^3-3x^5

extreme f(x,y)=9x^2+y^2

Frequently Asked Questions (FAQ)

What is the extreme (1-x^2)^2 ?
The extreme (1-x^2)^2 is Minimum(-1,0),Maximum(0,1),Minimum(1,0)