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Popular >

extreme x/(e^x)

Solution

extreme points

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

Solution

Maximum (1, \frac{1}{e})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = 1

into

\frac{x}{e ^{x}} : \frac{1}{e}

Maximum (1, \frac{1}{e})

Popular Examples

extreme f(x)=(x^8)/(e^{7x)}extreme points

f (x) = \frac{x ^{8}}{e ^{7 x}}

extreme-5/(1+x^2)extreme points

- \frac{5}{1 + x ^{2}}

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

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

extreme f(x)=-1/6 x^3+3/2 x^2+5/2 x-11/6 extreme points

f (x) = - \frac{1}{6} x^{3} + \frac{3}{2} x^{2} + \frac{5}{2} x - \frac{11}{6}

extreme f(x)=3x-t extreme points

f (x) = 3 x - t

Frequently Asked Questions (FAQ)

What is the extreme x/(e^x) ?
The extreme x/(e^x) is Maximum(1, 1/e)