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Popular >

extreme f(x)=(x+1/x)

Solution

extreme points

f (x) = (x + \frac{1}{x})

Solution

Maximum (- 1, - 2), Minimum (1, 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

x + \frac{1}{x} : - 2

Maximum (- 1, - 2)

Plug

x = 1

into

x + \frac{1}{x} : 2

Minimum (1, 2)

Maximum (- 1, - 2), Minimum (1, 2)

Popular Examples

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f (x) = x^{2} + y^{2} + x + y + x y

extreme f(x)=(ln(x))/(8x),1<= x<= 4 extreme points

f (x) = \frac{ln ( x )}{8 x}, 1 \leq x \leq 4

extreme f(x)=(1+3x)/(sqrt(4+5x^2))extreme points

f (x) = \frac{1 + 3 x}{4 + 5 x ^{2}}

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

extreme f(x)=(2x^2+1)^2 extreme points

f (x) = (2 x^{2} + 1)^{2}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x+1/x) ?
The extreme f(x)=(x+1/x) is Maximum(-1,-2),Minimum(1,2)