InterviewSolution
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InterviewSolution
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Show that the function `f(x)={:{(1+x ", " x le2","),(5-x", "x gt2):}` is not differentiable at x=2 |
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Answer» R.f(2) `=underset(hrarr0)lim((f2+h)-f(2))/(h)` `=underset(hrarr0)lim({5-(2+h)}-(1+2))/h` `=underset(hrarr0)lim(-h)/h=underset(hrarr0)lim(-1)=-1` and L.f(2) `=underset(hrarr0)lim(f(2-h)-f(2))/(-h)` `=underset(hrarr0)lim({1+(2-h)}-(1+2))/(-h)` `=underset(hrarr0)lim(-h)/(-h)lim(1)=1` `therefore R.f(2) ne L.f(2)` `therefore` f(x) is not differentiable at x=2. |
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