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Popular >

extreme f(x)=1+1/x+7/(x^2)+1/(x^3)

Solution

extreme points

f (x) = 1 + \frac{1}{x} + \frac{7}{x ^{2}} + \frac{1}{x ^{3}}

Solution

Minimum (- 7 - 46, \frac{16821 - 2484 46}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1), Maximum (- 7 + 46, \frac{2484 46 + 16821}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1)

Solution steps

f^{'} (x) = - \frac{1}{x ^{2}} - \frac{14}{x ^{3}} - \frac{3}{x ^{4}}

Find intervals:

Decreasing

: - \infty < x < - 7 - 46,

Increasing

: - 7 - 46 < x < - 7 + 46,

Decreasing

: - 7 + 46 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 7 - 46

into

1 + \frac{1}{x} + \frac{7}{x ^{2}} + \frac{1}{x ^{3}} : \frac{16821 - 2484 46}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1

Minimum (- 7 - 46, \frac{16821 - 2484 46}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1)

Plug

x = - 7 + 46

into

1 + \frac{1}{x} + \frac{7}{x ^{2}} + \frac{1}{x ^{3}} : \frac{2484 46 + 16821}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1

Maximum (- 7 + 46, \frac{2484 46 + 16821}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1)

Minimum (- 7 - 46, \frac{16821 - 2484 46}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1), Maximum (- 7 + 46, \frac{2484 46 + 16821}{342693 5 ^{2} - 50527 4 ^{2} \cdot 46} + 1)

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Frequently Asked Questions (FAQ)

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