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Popular >

extreme y=x+1/x

Solution

extreme points

y = 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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2 x + 1 + \frac{5}{x - 5}

extreme f(x)=(x-y)(1-xy)extreme points

f (x) = (x - y) (1 - x y)

extreme f(x,y)=2x^2+y^2 extreme points

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

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

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

extreme xsqrt(x^2+25)extreme points

x x^{2} + 25

Frequently Asked Questions (FAQ)

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