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Popular Functions >

extreme 2x^2-x^4

Solution

extreme points

2 x^{2} - x^{4}

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

2 x^{2} - x^{4} : 1

Maximum (- 1, 1)

Plug

x = 0

into

2 x^{2} - x^{4} : 0

Minimum (0, 0)

Plug

x = 1

into

2 x^{2} - x^{4} : 1

Maximum (1, 1)

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

Graph

Popular Examples

extreme f(x,y)=-3x^2+6x+12xy-3y^2+2y^3+6

extreme f(x)=6xe^{-0.6x}

extreme f(x)=(e^{x-1})/x

extreme f(x,y)=sqrt(4-x^2-y^2)+sqrt(1-y^2)

extreme f(x)=-x^2-8x-12

Frequently Asked Questions (FAQ)

What is the extreme 2x^2-x^4 ?
The extreme 2x^2-x^4 is Maximum(-1,1),Minimum(0,0),Maximum(1,1)