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Let f:R to R be defined by f(x)={{:(2k...

Let `f:R to R` be defined by
`f(x)={{:(2k-2x",",ifxle-1),(2x+3",",iffxgt-1):}`
If f has a local minimum at x=-1, then a possible value of k is

A

`-1//2`

B

`-1`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
If f(x) has a local minimum at x=-1 then
`underset(x rarr -1^+)lim f(x)= underset(x rarr -1-)lim f(X)`
`rArr underset(x rarr -1^+)lim 2x+3=underset(x rarr -1^-) k-2x `
`rArr -2 +3 =k+2 rArr k=-1`
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