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Popular >

extreme f(x)=x*ln(x)

Solution

extreme points

f (x) = x \cdot ln (x)

Solution

Minimum (\frac{1}{e}, - \frac{1}{e})

Solution steps

f^{'} (x) = ln (x) + 1

Find intervals:

Decreasing

: 0 < x < \frac{1}{e},

Increasing

: \frac{1}{e} < x < \infty

Plug

x = \frac{1}{e}

into

x \cdot ln (x) : - \frac{1}{e}

Minimum (\frac{1}{e}, - \frac{1}{e})

Popular Examples

extreme f(x)=(cos(x)-0.5)^2 extreme points

f (x) = (cos (x) - 0.5)^{2}

extreme f(x)=-x^3+6x^2-10x+4 extreme points

f (x) = - x^{3} + 6 x^{2} - 10 x + 4

extreme f(x)=4x^3-3x^2-6x+3 extreme points

f (x) = 4 x^{3} - 3 x^{2} - 6 x + 3

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

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

extreme (x^2)/(x-5)extreme points

\frac{x ^{2}}{x - 5}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x*ln(x) ?
The extreme f(x)=x*ln(x) is Minimum(1/e ,-1/e)