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Popular >

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

Solution

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

Solution steps

Domain of

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

Range of

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

Axis interception points of

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

X Intercepts

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

Y Intercepts

: (0, 1)

Asymptotes of

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

Horizontal

: y = 0

Extreme Points of

e^{- x^{2}} - 2 e^{- x^{2}} 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}}})

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Frequently Asked Questions (FAQ)

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