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Popular >

extreme x^4-2x^2+1

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x^{4} - 2 x^{2} + 1 : 0

Minimum (- 1, 0)

Plug

x = 0

into

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

Maximum (0, 1)

Plug

x = 1

into

x^{4} - 2 x^{2} + 1 : 0

Minimum (1, 0)

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

Popular Examples

extreme y=6sqrt(3)x+12cos(x)extreme points

y = 63 x + 12 cos (x)

extreme f(x,y)=x^2+7y^2+x-6y+4 extreme points

f (x, y) = x^{2} + 7 y^{2} + x - 6 y + 4

extreme f(x)=2x^2ln(x)-19x^2 extreme points

f (x) = 2 x^{2} ln (x) - 19 x^{2}

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

f (x, y) = x^{2} + 9 x y + y^{2}

extreme f(x)=x^4-12x^3+4 extreme points

f (x) = x^{4} - 12 x^{3} + 4

Frequently Asked Questions (FAQ)

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