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Popular >

extreme f(x)=1+1/x+5/(x^2)+1/(x^3)

Solution

extreme points

f (x) = 1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}}

Solution

Minimum (- 5 - 22, \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1), Maximum (- 5 + 22, \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Solution steps

f^{'} (x) = - \frac{1}{x ^{2}} - \frac{10}{x ^{3}} - \frac{3}{x ^{4}}

Find intervals:

Decreasing

: - \infty < x < - 5 - 22,

Increasing

: - 5 - 22 < x < - 5 + 22,

Decreasing

: - 5 + 22 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 5 - 22

into

1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}} : \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1

Minimum (- 5 - 22, \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Plug

x = - 5 + 22

into

1 + \frac{1}{x} + \frac{5}{x ^{2}} + \frac{1}{x ^{3}} : \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1

Maximum (- 5 + 22, \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Minimum (- 5 - 22, \frac{5535 - 1188 22}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1), Maximum (- 5 + 22, \frac{1188 22 + 5535}{41402 3 ^{2} - 8827 0 ^{2} \cdot 22} + 1)

Popular Examples

extreme f(x)=(x^2-0.8x+0.32)/(1.6-2x)extreme points

f (x) = \frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x}

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

extreme f(x)=|(x-2)/(x+5)|-3 extreme points

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extreme 2x^4-x^2+5 extreme points

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f (x) = 7 x^{9} - 9 x^{7} - 5 (- 3.4)

Frequently Asked Questions (FAQ)

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