What is the extreme f(x)=3x^4-6x^2+7 ?

The extreme f(x)=3x^4-6x^2+7 is Minimum(-1,4),Maximum(0,7),Minimum(1,4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=3x^4-6x^2+7

extreme

Minimum (- 1, 4), Maximum (0, 7), Minimum (1, 4)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

3 x^{4} - 6 x^{2} + 7 : 4

Minimum (- 1, 4)

Plug

x = 0

into

3 x^{4} - 6 x^{2} + 7 : 7

Maximum (0, 7)

Plug

x = 1

into

3 x^{4} - 6 x^{2} + 7 : 4

Minimum (1, 4)

Minimum (- 1, 4), Maximum (0, 7), Minimum (1, 4)

What is the extreme f(x)=3x^4-6x^2+7 ?
The extreme f(x)=3x^4-6x^2+7 is Minimum(-1,4),Maximum(0,7),Minimum(1,4)