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Popular >

extreme f(x)=(e^{x-1})/x

Solution

extreme points

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

Solution

Minimum (1, 1)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 1

into

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

Minimum (1, 1)

Popular Examples

extreme f(x)=(x^3)/(x^2-81)extreme points

f (x) = \frac{x ^{3}}{x ^{2} - 81}

extreme f(x,y)=sqrt(4-x^2-y^2)+sqrt(1-y^2)extreme points

f (x, y) = 4 - x^{2} - y^{2} + 1 - y^{2}

extreme f(x)=-x^2-8x-12 extreme points

f (x) = - x^{2} - 8 x - 12

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

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

extreme f(x)=x^3+3x^2-45x+100 extreme points

f (x) = x^{3} + 3 x^{2} - 45 x + 100

Frequently Asked Questions (FAQ)

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