1.

Show that f(x) = |x| is not differentiableat x =0

Answer»

SOLUTION :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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