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Show that f(x)=|x| is not differentiable...

Show that `f(x)=|x|` is not differentiable at `x=0` .

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Left hand derivative at x =0
` underset (x to 0^(-)) (f (x) -f(0))/ (x -0) `
` underset(h to 0) (f (0 -h) -f(0))/ ( 0-h-0) `
` underset( h to 0) h/(-h) = -1 `
(ii) Right hand derivative at x =0
` underset(x to 0^(+)) lim (f(x) -f(0))/(x -0) `
`underset(h to 0) lim (f (0+h)-f(0))/ (0+h-0)`
` underset( h to 0) h / h =1`
Since LHD ` ne ` RHD
THe function is not differentiable at x =0
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