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Popular >

extreme f(x)=2x^4+6x^3-12x^2+8

Solution

extreme points

f (x) = 2 x^{4} + 6 x^{3} - 12 x^{2} + 8

Solution

Minimum (\frac{- 9 - 273}{8}, - \frac{9 ( 1619 + 91 273 )}{256} + 8), Maximum (0, 8), Minimum (\frac{- 9 + 273}{8}, \frac{9 ( 91 273 - 1619 )}{256} + 8)

Solution steps

f^{'} (x) = 8 x^{3} + 18 x^{2} - 24 x

Find intervals:

Decreasing

: - \infty < x < \frac{- 9 - 273}{8},

Increasing

: \frac{- 9 - 273}{8} < x < 0,

Decreasing

: 0 < x < \frac{273 - 9}{8},

Increasing

: \frac{273 - 9}{8} < x < \infty

Plug

x = \frac{- 9 - 273}{8}

into

2 x^{4} + 6 x^{3} - 12 x^{2} + 8 : - \frac{9 ( 1619 + 91 273 )}{256} + 8

Minimum (\frac{- 9 - 273}{8}, - \frac{9 ( 1619 + 91 273 )}{256} + 8)

Plug

x = 0

into

2 x^{4} + 6 x^{3} - 12 x^{2} + 8 : 8

Maximum (0, 8)

Plug

x = \frac{- 9 + 273}{8}

into

2 x^{4} + 6 x^{3} - 12 x^{2} + 8 : \frac{9 ( 91 273 - 1619 )}{256} + 8

Minimum (\frac{- 9 + 273}{8}, \frac{9 ( 91 273 - 1619 )}{256} + 8)

Minimum (\frac{- 9 - 273}{8}, - \frac{9 ( 1619 + 91 273 )}{256} + 8), Maximum (0, 8), Minimum (\frac{- 9 + 273}{8}, \frac{9 ( 91 273 - 1619 )}{256} + 8)

Popular Examples

monotone f(x)=-sqrt(x+3)monotone intervals

f (x) = - x + 3

slope ofintercept 5x-15y=17 slope intercept

5 x - 15 y = 17

critical f(x)=(8-4x)e^x critical points

f (x) = (8 - 4 x) e^{x}

domain of sin(arccos(x))domain

sin (arccos (x))

line (-8,5),(17,8)line

(- 8, 5), (17, 8)

Frequently Asked Questions (FAQ)

What is the extreme f(x)=2x^4+6x^3-12x^2+8 ?
The extreme f(x)=2x^4+6x^3-12x^2+8 is