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Popular >

f(x)=x+e^{-3x},-1<= x<= 3

Solution

f (x) = x + e^{- 3 x}, - 1 \leq x \leq 3

Solution

Domain : - 1 \leq x \leq 3

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

Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Maximum (- 1, - 1 + e^{3}), Minimum (\frac{ln ( 3 )}{3}, \frac{ln ( 3 ) + 1}{3}), Maximum (3, 3 + \frac{1}{e ^{9}})

+1

Interval Notation

Domain : [- 1, 3]

Range : [\frac{ln ( 3 ) + 1}{3}, - 1 + e^{3}]

Solution steps

Domain of

x + e^{- 3 x}, - 1 \leq x \leq 3 : - 1 \leq x \leq 3

Range of

x + e^{- 3 x}, - 1 \leq x \leq 3 : \frac{ln ( 3 ) + 1}{3} \leq f (x) \leq - 1 + e^{3}

Axis interception points of

x + e^{- 3 x}, - 1 \leq x \leq 3 :

Y Intercepts

: (0, 1)

Asymptotes of

x + e^{- 3 x}, - 1 \leq x \leq 3 :

None

Extreme Points of

x + e^{- 3 x}, - 1 \leq x \leq 3 :

Maximum

(- 1, - 1 + e^{3}),

Minimum

(\frac{ln ( 3 )}{3}, \frac{ln ( 3 ) + 1}{3}),

Maximum

(3, 3 + \frac{1}{e ^{9}})

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Frequently Asked Questions (FAQ)

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