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Popular Calculus >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \leq - 2 e^{- 2 + 2} + 22 e^{- 2 + 2}

X Intercepts : (0, 0), (2, 0), Y Intercepts : (0, 0)

Asymptotes : Horizontal y = 0

Extreme Points : Maximum (2 - 2, - 2 e^{- 2 + 2} + 22 e^{- 2 + 2}), Minimum (2 + 2, - 2 e^{- 2 - 2} - 22 e^{- 2 - 2})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : (- \infty, - 2 e^{- 2 + 2} + 22 e^{- 2 + 2}]

Solution steps

Domain of

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

Range of

2 e^{- x} x - e^{- x} x^{2} : f (x) \leq - 2 e^{- 2 + 2} + 22 e^{- 2 + 2}

Axis interception points of

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

X Intercepts

: (0, 0), (2, 0),

Y Intercepts

: (0, 0)

Asymptotes of

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

Horizontal

: y = 0

Extreme Points of

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

Maximum

(2 - 2, - 2 e^{- 2 + 2} + 22 e^{- 2 + 2}),

Minimum

(2 + 2, - 2 e^{- 2 - 2} - 22 e^{- 2 - 2})

Graph

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Frequently Asked Questions (FAQ)

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