en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : - \frac{2}{e ^{\frac{3}{2}}} \leq f (x) \leq 1

X Intercepts : (- \frac{1}{2}, 0), (\frac{1}{2}, 0), Y Intercepts : (0, 1)

Asymptotes : Horizontal y = 0

Extreme Points : Minimum (- \frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}}), Maximum (0, 1), Minimum (\frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{2}{e ^{\frac{3}{2}}}, 1]

Solution steps

Domain of

e^{- x^{2}} - 2 x^{2} e^{- x^{2}} : - \infty < x < \infty

Range of

e^{- x^{2}} - 2 x^{2} e^{- x^{2}} : - \frac{2}{e ^{\frac{3}{2}}} \leq f (x) \leq 1

Axis interception points of

e^{- x^{2}} - 2 x^{2} e^{- x^{2}} :

X Intercepts

: (- \frac{1}{2}, 0), (\frac{1}{2}, 0),

Y Intercepts

: (0, 1)

Asymptotes of

e^{- x^{2}} - 2 x^{2} e^{- x^{2}} :

Horizontal

: y = 0

Extreme Points of

e^{- x^{2}} - 2 x^{2} e^{- x^{2}} :

Minimum

(- \frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}}),

Maximum

(0, 1),

Minimum

(\frac{3}{2}, - \frac{2}{e ^{\frac{3}{2}}})

Popular Examples

y=sqrt(x^2-x^4)

y = x^{2} - x^{4}

F (x) = x^{3} + x

f(x)=sqrt((1-cos(4x))/2)

f (x) = \frac{1 - cos ( 4 x )}{2}

y=(1-x)/(1+x^2)

y = \frac{1 - x}{1 + x ^{2}}

f(x)=(3-x)/(x-1)

f (x) = \frac{3 - x}{x - 1}

Frequently Asked Questions (FAQ)

What is the f(x)=e^{-x^2}-2x^2e^{-x^2} ?
The f(x)=e^{-x^2}-2x^2e^{-x^2} is