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f(x) = x(x+3)e^(-x//2) in [-3,0]...

`f(x) = x(x+3)e^(-x//2)` in `[-3,0]`

A

0

B

`-1`

C

`-2`

D

`-3`

Text Solution

Verified by Experts

The correct Answer is:
C
It is given that f(x) satisfies all the condition of Rolle's theorem. So, there exists `c in (-3,0)` such that `f'(c)=0`
Now,
`f'(x)=(2x+3x)e^(-2x//3)-(x)/(2)(x+3)e^(-x//2)`
`rArr f'(x)=(e^(-x//2))/(2)(-x^(2)+x+6)`
`:. f'(x)=0"for" c=-2`
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OBJECTIVE RD SHARMA ENGLISH-MEAN VALUE THEOREMS-Exercise
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  21. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

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