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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` |
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Answer» Correct Answer - 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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