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Popular >

extreme ln(x^2+144)

Solution

extreme points

ln (x^{2} + 144)

Solution

Minimum (0, 2 ln (12))

Solution steps

f^{'} (x) = \frac{2 x}{x ^{2} + 144}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug

x = 0

into

ln (x^{2} + 144) : 2 ln (12)

Minimum (0, 2 ln (12))

Popular Examples

extreme f(x,y)=-5x^2-3y^2+48x-4y+2xy+300 extreme points

f (x, y) = - 5 x^{2} - 3 y^{2} + 48 x - 4 y + 2 x y + 300

extreme f(x,y)=sqrt(400-49x^2-100y^2)extreme points

f (x, y) = 400 - 49 x^{2} - 100 y^{2}

extreme f(x)=3x^4-8x^3-144x^2+1 extreme points

f (x) = 3 x^{4} - 8 x^{3} - 144 x^{2} + 1

extreme f(x,y)=-5x^2-5xy-7y^2+50x-67y+9 extreme points

f (x, y) = - 5 x^{2} - 5 x y - 7 y^{2} + 50 x - 67 y + 9

extreme y=x^2+2x+2 extreme points

y = x^{2} + 2 x + 2

Frequently Asked Questions (FAQ)

What is the extreme ln(x^2+144) ?
The extreme ln(x^2+144) is Minimum(0,2ln(12))