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Popular >

extreme f(x)= x/(e^x)

Solution

extreme points

f (x) = \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)=3(x-5)^2+1 extreme points

f (x) = 3 (x - 5)^{2} + 1

extreme f(x,y)=2x^2+y^2+8x-6y+20 extreme points

f (x, y) = 2 x^{2} + y^{2} + 8 x - 6 y + 20

extreme f(x,y)=3x+4xy+2y^3-8 extreme points

f (x, y) = 3 x + 4 x y + 2 y^{3} - 8

extreme f(x)=(4x)/(3x^2+27)extreme points

f (x) = \frac{4 x}{3 x ^{2} + 27}

extreme f(x)= 1/3 x^3+2x^2+4x extreme points

f (x) = \frac{1}{3} x^{3} + 2 x^{2} + 4 x

Frequently Asked Questions (FAQ)

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