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If f(x) = { 3 + |x-k|, x leq k; a^2 -2 +...

If `f(x) = { 3 + |x-k|, x leq k; a^2 -2 + sin(x-k)/(x-k), xgtk}` has minimum at x =k, then show that `|a| >2`.

A

`aepsilonR`

B

`|a|lt2`

C

`|a|gt2`

D

`1lt|a|lt2`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(k)=3`
`f(k+h)=a^(2)-2+(sinh)/himplieslim_(hrarro) f(k+h)=a^(2)-1`
`lim_(xrarr0) f(k-h)=lim_(hrarr0)(3+|k-h-k|)=lim_(hrarr0)(3+|-h|)=3`
`impliesa^(2)-1gt3`
`a^(2)gt4rarr|a|gt2`
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