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Let f:""RvecR be defined by f(x)""={k-2x...

Let `f:""RvecR` be defined by `f(x)""={k-2x , if""xlt=-1 2x+3,f""x >-1}` . If f has a local minimum at `x""=""1` , then a possible value of k is (1) 0 (2) `-1/2` (3) `-1` (4) 1

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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