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Popular >

extreme x^4-2x^2

Solution

extreme points

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

Solution

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

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

Minimum (- 1, - 1)

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = 1

into

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

Minimum (1, - 1)

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

Popular Examples

extreme f(x)=e^x+x^2 extreme points

f (x) = e^{x} + x^{2}

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

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

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

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

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

f (x, y) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

extreme f(x)=x^{1/3}(x+4)extreme points

f (x) = x^{\frac{1}{3}} (x + 4)

Frequently Asked Questions (FAQ)

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