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Popular >

extreme y=(x^2+1)/x

Solution

extreme points

y = \frac{x ^{2} + 1}{x}

Solution

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

Solution steps

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

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

Maximum (- 1, - 2)

Plug

x = 1

into

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

Minimum (1, 2)

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

Popular Examples

extreme f(x)=x^3-12x^2-27x+2,-2<= x<= 10 extreme points

f (x) = x^{3} - 12 x^{2} - 27 x + 2, - 2 \leq x \leq 10

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

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

extreme f(x,y)=x^2+9 extreme points

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

extreme f(x)=-x^2+3xy-8y^2-5x+42y+9 extreme points

f (x) = - x^{2} + 3 x y - 8 y^{2} - 5 x + 42 y + 9

derivative of In\sqrt[3]{6x+4}

Frequently Asked Questions (FAQ)

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