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Popular Functions >

extreme f(x)=(e^x)/(x^2)

Solution

extreme points

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

Solution

Minimum (2, \frac{e ^{2}}{4})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 2

into

\frac{e ^{x}}{x ^{2}} : \frac{e ^{2}}{4}

Minimum (2, \frac{e ^{2}}{4})

Graph

Popular Examples

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intercepts of (x-4)^3+6

domain of (2x^2-3)/5

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(e^x)/(x^2) ?
The extreme f(x)=(e^x)/(x^2) is Minimum(2,(e^2)/4)