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Popular >

extreme f(x)=(2+4x^2)/(1-3x)

Solution

extreme points

f (x) = \frac{2 + 4 x ^{2}}{1 - 3 x}

Solution

Minimum (- \frac{- 2 + 22}{6}, \frac{44 2 - 8 11}{9 11}), Maximum (\frac{2 + 22}{6}, - \frac{44 2 + 8 11}{9 11})

Solution steps

f^{'} (x) = \frac{- 12 x ^{2} + 8 x + 6}{( 1 - 3 x ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < \frac{2 - 22}{6},

Increasing

: \frac{2 - 22}{6} < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \frac{2 + 22}{6},

Decreasing

: \frac{2 + 22}{6} < x < \infty

Plug

x = - \frac{- 2 + 22}{6}

into

\frac{2 + 4 x ^{2}}{1 - 3 x} : \frac{44 2 - 8 11}{9 11}

Minimum (- \frac{- 2 + 22}{6}, \frac{44 2 - 8 11}{9 11})

Plug

x = \frac{2 + 22}{6}

into

\frac{2 + 4 x ^{2}}{1 - 3 x} : - \frac{44 2 + 8 11}{9 11}

Maximum (\frac{2 + 22}{6}, - \frac{44 2 + 8 11}{9 11})

Minimum (- \frac{- 2 + 22}{6}, \frac{44 2 - 8 11}{9 11}), Maximum (\frac{2 + 22}{6}, - \frac{44 2 + 8 11}{9 11})

Popular Examples

extreme f(x)=6x+(24)/(x^2)+5,x>0 extreme points

f (x) = 6 x + \frac{24}{x ^{2}} + 5, x > 0

extreme f(x)=-5x^{+30x+1}extreme points

f (x) = - 5 x^{+ 30 x + 1}

extreme f(x,y)=3x-5y-2 extreme points

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extreme f(x)=x^3-2x^2-6x+1 extreme points

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extreme f(x)=-20x^2-25y^2+440x+250y+150 extreme points

f (x) = - 20 x^{2} - 25 y^{2} + 440 x + 250 y + 150

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(2+4x^2)/(1-3x) ?
The extreme f(x)=(2+4x^2)/(1-3x) is