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Popular >

extreme x^4-2x^2+2

Solution

extreme points

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

Solution

Minimum (- 1, 1), Maximum (0, 2), 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} + 2 : 1

Minimum (- 1, 1)

Plug

x = 0

into

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

Maximum (0, 2)

Plug

x = 1

into

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

Minimum (1, 1)

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

Popular Examples

extreme f(x)=x^{3/2},(-1,2)extreme points

f (x) = x^{\frac{3}{2}}, (- 1, 2)

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

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

extreme f(x)=(x+1)/(x^2+3)extreme points

f (x) = \frac{x + 1}{x ^{2} + 3}

extreme f(x,y)=e^{5xy}extreme points

f (x, y) = e^{5 x y}

extreme f(x,y)=2x-y extreme points

f (x, y) = 2 x - y

Frequently Asked Questions (FAQ)

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