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The complete set of values of x for whic...

The complete set of values of `x` for which
`(x^(3)(x-1)^(2)(x+4))/((x+1)(x-3)) ge 0` is

A

A. `(-oo,-4] uu (-1,0] uu (3,oo) uu {1}`

B

B. `(-oo,-4] uu (-1,0] uu (3,oo) uu {-1}`

C

C. `[-4,-1) uu [0,1) uu (3,oo) `

D

D. `[-4,-1) uu [0,1] uu (3,oo) `

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` We have `E=(x^(3)(x-1)^(2)(x+4))/((x+1)(x-3))`
Sign scheme of `E` is as shown below.

At `x=1`, sign of the expression does not change as `(x-1)` has power `'2'`.
From the sign scheme.
`x in(-oo,-4]uu(-1,0]uu(3,oo)uu{1}`
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