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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

B

1

C

0

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
1
`f(X)={{:(k-2x, if xle-1),(2x+3,if xgt-1):}`
For minima at x=-1 we must have
`underset(xrarr-1)limf(x)leunderset(xrarr1^(+))limf(x)`
`rarr k+2le1`
`rarr kle-1`
`rarrk=-1`
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