InterviewSolution
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InterviewSolution
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A function f(x) is defined in the interval [1,4) as follows `f(x)={{:(,log_(e)[x],1 le x lt 3),(,|log_(e)x|,3 le x lt 4):}`. Then, the curve y=f(x)A. is broken at two pointsB. is broken at exactly one pointC. does not have a definite tangent at two pointsD. does not have a definite tangent at more than two points |
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Answer» Correct Answer - A::C We have `f(x)={{:(,log_(e)[x],1 le x lt 3),(,|log_(e)x|,3 le x lt 4):}` `Rightarrow f(x)={{:(,0,1 le x lt 2),(,log_(e)2,2 le x lt 3),(,|log_(e)x|,3 le x lt 4):}` Clearly, f(x) is everywhere continuous and differentiable except possibility at x=2,3 We observe that `underset(x to 2^(-))lim f(x)=underset(x to2^(-))lim 0=0` `and underset(x to 2^(+))lim f(x)=underset(x to2^(+))lim log_(e)2=log_(e)2` Clearly, f(x) is not continuous at x=2 It can be easily seen that f(x) is not continuous at x=3 Hence, f(x) is neither continuous nor differenitable at x=2,3 Thus, the curve y=f(x) is broken at two points and it does not have a definite tangent at these points |
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