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Popular >

inflection e^{1/x}

Solution

inflection points

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

Solution

(- \frac{1}{2}, \frac{1}{e ^{2}})

Solution steps

f^{''} (x) = - \frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{4}}

Find intervals:

Concave Downward

: - \infty < x < - \frac{1}{2},

Concave Upward

: - \frac{1}{2} < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - \frac{1}{2}

into

e^{\frac{1}{x}} : \frac{1}{e ^{2}}

(- \frac{1}{2}, \frac{1}{e ^{2}})

Popular Examples

extreme (x^2-5)/(x-3)extreme points

\frac{x ^{2} - 5}{x - 3}

inflection 3x^{2/3}-2x inflection points

3 x^{\frac{2}{3}} - 2 x

inverse of f(x)=(x-7)/(x+1)inverse

f (x) = \frac{x - 7}{x + 1}

range of f(x)=((8x-3))/x range

f (x) = \frac{( 8 x - 3 )}{x}

domain of f(x)= x/(sqrt(25-x^2))domain

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

Frequently Asked Questions (FAQ)

What is the inflection e^{1/x} ?
The inflection e^{1/x} is (-1/2 , 1/(e^2))