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Popular >

extreme x^4-2x^2+9

Solution

extreme points

x^{4} - 2 x^{2} + 9

Solution

Minimum (- 1, 8), Maximum (0, 9), Minimum (1, 8)

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} + 9 : 8

Minimum (- 1, 8)

Plug

x = 0

into

x^{4} - 2 x^{2} + 9 : 9

Maximum (0, 9)

Plug

x = 1

into

x^{4} - 2 x^{2} + 9 : 8

Minimum (1, 8)

Minimum (- 1, 8), Maximum (0, 9), Minimum (1, 8)

Popular Examples

extreme (x^2)/(x-3)extreme points

\frac{x ^{2}}{x - 3}

extreme x^4-2x^2+2 extreme points

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

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}

Frequently Asked Questions (FAQ)

What is the extreme x^4-2x^2+9 ?
The extreme x^4-2x^2+9 is Minimum(-1,8),Maximum(0,9),Minimum(1,8)