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Popular >

extreme (e^x)/x

Solution

extreme points

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

Solution

Minimum (1, e)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

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

Minimum (1, e)

Popular Examples

extreme f(x,y)=2x^2-8x+y^2+16y+100 extreme points

f (x, y) = 2 x^{2} - 8 x + y^{2} + 16 y + 100

extreme f(x,y)= 1/(sqrt(25-x^2-y^2))extreme points

f (x, y) = \frac{1}{25 - x ^{2} - y ^{2}}

extreme f(x)=sqrt(1-x^2)extreme points

f (x) = 1 - x^{2}

extreme f(x,y)=4x^2y+2xy^2-12xy-5 extreme points

f (x, y) = 4 x^{2} y + 2 x y^{2} - 12 x y - 5

extreme f(x)=x^3+(48)/x extreme points

f (x) = x^{3} + \frac{48}{x}

Frequently Asked Questions (FAQ)

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