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Popular >

extreme f(x)=x^2-2ln(x)

Solution

extreme points

f (x) = x^{2} - 2 ln (x)

Solution

Minimum (1, 1)

Solution steps

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

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

x^{2} - 2 ln (x) : 1

Minimum (1, 1)

Graph

Popular Examples

extreme f(x)=(2e^x)/(x^5)extreme points

f (x) = \frac{2 e ^{x}}{x ^{5}}

extreme f(x,y)=(9x^2+7x+10)(9y^2+4y+9)extreme points

f (x, y) = (9 x^{2} + 7 x + 10) (9 y^{2} + 4 y + 9)

extreme f(x)=4x^2-2x+1 extreme points

f (x) = 4 x^{2} - 2 x + 1

extreme a+(ln(x))^2 extreme points

a + (ln (x))^{2}

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

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^2-2ln(x) ?
The extreme f(x)=x^2-2ln(x) is Minimum(1,1)