What is the extreme-x^4+x^2 ?

The extreme-x^4+x^2 is Maximum(-1/(sqrt(2)), 1/4),Minimum(0,0),Maximum(1/(sqrt(2)), 1/4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme-x^4+x^2

extreme points

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

Maximum (- \frac{1}{2}, \frac{1}{4}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{4})

Solution steps

f^{'} (x) = - 4 x^{3} + 2 x

Find intervals:

Increasing

: - \infty < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < 0,

Increasing

: 0 < x < \frac{1}{2},

Decreasing

: \frac{1}{2} < x < \infty

Plug

x = - \frac{1}{2}

into

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

Maximum (- \frac{1}{2}, \frac{1}{4})

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{1}{2}

into

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

Maximum (\frac{1}{2}, \frac{1}{4})

Maximum (- \frac{1}{2}, \frac{1}{4}), Minimum (0, 0), Maximum (\frac{1}{2}, \frac{1}{4})

f (x, y) = x y - x^{2} - y^{2} + 3 + 9 y

f (x) = x^{2} + 3 x - 7

f (0) = x^{2} - 2 x - 3

x^{4} - 16 x^{2} + 3

f (x) = 8 - 5 x + x^{2}

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