InterviewSolution
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InterviewSolution
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Show that the function f(x)=|x-2| is continuous but not differentiable at x=2. |
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Answer» `f(x)=abs(x-2)={:{(x-2 ", " x ge 2),(-(x-2)", "x lt2):}` `R.H.L=underset(xrarr2^+)(lim)f(x)=underset(hrarr0)limf(2+h)` `=underset(xrarr0)(lim)f(2+h-2)=underset(hrarr0)limf(2+h)` f(2)2-2=0 and `L.H.L=underset(xrarr2^-)(lim)f(x)=underset(hrarr0)limf(2-h)` `=underset(hrarr0)(lim)-(2+h-2)=underset(hrarr0)limh(2-h)` `therefore`R.H.L = L.H.L=f(2) `therefore` f(x) is not differentialble at x=2. |
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