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Popular >

extreme x^4-2x^2+3

Solution

extreme points

x^{4} - 2 x^{2} + 3

Solution

Minimum (- 1, 2), Maximum (0, 3), Minimum (1, 2)

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} + 3 : 2

Minimum (- 1, 2)

Plug

x = 0

into

x^{4} - 2 x^{2} + 3 : 3

Maximum (0, 3)

Plug

x = 1

into

x^{4} - 2 x^{2} + 3 : 2

Minimum (1, 2)

Minimum (- 1, 2), Maximum (0, 3), Minimum (1, 2)

Popular Examples

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

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

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

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

extreme f(x)=xln(y^2-x)extreme points

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

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

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

extreme f(x)=x^3-12x^2 extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme x^4-2x^2+3 ?
The extreme x^4-2x^2+3 is Minimum(-1,2),Maximum(0,3),Minimum(1,2)