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Popular >

extreme f(x)= 1/x+x

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, - 2)

Plug

x = 1

into

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

Minimum (1, 2)

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

Graph

Popular Examples

extreme f(x)=(x/5)^5-((4x)/4)^4+5 extreme points

f (x) = (\frac{x}{5})^{5} - (\frac{4 x}{4})^{4} + 5

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

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

extreme f(x)=2x+4y extreme points

f (x) = 2 x + 4 y

extreme f(x)=x^4-2x^3-11x^2+12x+36 extreme points

f (x) = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36

extreme y=9x^3-7 extreme points

y = 9 x^{3} - 7

Frequently Asked Questions (FAQ)

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