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Popular >

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

Solution

extreme points

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

Solution

Minimum (\frac{- 1 - 65}{8}, - \frac{1633 + 65 65}{256} + 3), Maximum (0, 3), Minimum (\frac{- 1 + 65}{8}, \frac{65 65 - 1633}{256} + 3)

Solution steps

f^{'} (x) = 24 x^{3} + 6 x^{2} - 24 x

Find intervals:

Decreasing

: - \infty < x < \frac{- 1 - 65}{8},

Increasing

: \frac{- 1 - 65}{8} < x < 0,

Decreasing

: 0 < x < \frac{65 - 1}{8},

Increasing

: \frac{65 - 1}{8} < x < \infty

Plug

x = \frac{- 1 - 65}{8}

into

6 x^{4} + 2 x^{3} - 12 x^{2} + 3 : - \frac{1633 + 65 65}{256} + 3

Minimum (\frac{- 1 - 65}{8}, - \frac{1633 + 65 65}{256} + 3)

Plug

x = 0

into

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

Maximum (0, 3)

Plug

x = \frac{- 1 + 65}{8}

into

6 x^{4} + 2 x^{3} - 12 x^{2} + 3 : \frac{65 65 - 1633}{256} + 3

Minimum (\frac{- 1 + 65}{8}, \frac{65 65 - 1633}{256} + 3)

Minimum (\frac{- 1 - 65}{8}, - \frac{1633 + 65 65}{256} + 3), Maximum (0, 3), Minimum (\frac{- 1 + 65}{8}, \frac{65 65 - 1633}{256} + 3)

Popular Examples

extreme f(x,y)=xy+(64)/x+(64)/y extreme points

f (x, y) = x y + \frac{64}{x} + \frac{64}{y}

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

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

extreme f(x,y)=5(x-3)^2-6y^2+4xy extreme points

f (x, y) = 5 (x - 3)^{2} - 6 y^{2} + 4 x y

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

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

extreme f(x,y)=ln(x)+ln(y)-ln(x+y)-x/(12)-y/3 extreme points

f (x, y) = ln (x) + ln (y) - ln (x + y) - \frac{x}{12} - \frac{y}{3}

Frequently Asked Questions (FAQ)

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