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Popular >

extreme f(x)=x-ln(1+x)

Solution

extreme points

f (x) = x - ln (1 + x)

Solution

Minimum (0, 0)

Solution steps

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

Find intervals:

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = 0

into

x - ln (1 + x) : 0

Minimum (0, 0)

Popular Examples

extreme f(x,y)=-1/(x-y)extreme points

f (x, y) = - \frac{1}{x - y}

extreme f(x)=x^4-14x^2-24x+1 extreme points

f (x) = x^{4} - 14 x^{2} - 24 x + 1

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

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

extreme f(x)=x^4-8x^2+5 extreme points

f (x) = x^{4} - 8 x^{2} + 5

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

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x-ln(1+x) ?
The extreme f(x)=x-ln(1+x) is Minimum(0,0)