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Popular >

extreme (e^{2x})/x

Solution

extreme points

\frac{e ^{2 x}}{x}

Solution

Minimum (\frac{1}{2}, 2 e)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = \frac{1}{2}

into

\frac{e ^{2 x}}{x} : 2 e

Minimum (\frac{1}{2}, 2 e)

Popular Examples

extreme 6x^2-12 extreme points

6 x^{2} - 12

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\frac{x ^{2} - 36}{x - 6}

extreme y=(x^2+14)^{1/3}extreme points

y = (x^{2} + 14)^{\frac{1}{3}}

extreme f(x)=(x-1)(x-17)^3+16,0<= x<= 10 extreme points

f (x) = (x - 1) (x - 17)^{3} + 16, 0 \leq x \leq 10

extreme f(x)=x+16y^2+xy-3y^2+25 extreme points

f (x) = x + 16 y^{2} + x y - 3 y^{2} + 25

Frequently Asked Questions (FAQ)

What is the extreme (e^{2x})/x ?
The extreme (e^{2x})/x is Minimum(1/2 ,2e)