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Popular >

extreme a+(ln(x))^2

Solution

extreme points

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

Solution

Minimum (1, a)

Solution steps

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

Find intervals:

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

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

Minimum (1, a)

Graph

Popular Examples

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

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

extreme f(x,y)=x^3-4x^2-4y^2+8xy-3x extreme points

f (x, y) = x^{3} - 4 x^{2} - 4 y^{2} + 8 x y - 3 x

extreme f(x)=x^3-3x^2-9x-3 extreme points

f (x) = x^{3} - 3 x^{2} - 9 x - 3

extreme f(x)=x^3-8x^2-12x+1 extreme points

f (x) = x^{3} - 8 x^{2} - 12 x + 1

extreme f(x)=3cos(x),0<= x<= 4pi extreme points

f (x) = 3 cos (x), 0 \leq x \leq 4 π

Frequently Asked Questions (FAQ)

What is the extreme a+(ln(x))^2 ?
The extreme a+(ln(x))^2 is Minimum(1,a)