Question

How to show `f(x)=|x|` It is differentiable everywhere except at the point x = 0 ?

Answer 1

`"See explanation"`

Explanation:

`"Apply the definition of |x| : "`
`f(x) = |x| =>`
`{ ( f(x) = x, x >= 0 ), ( f(x) = -x, x<= 0 ) :}`
`"Now derive : "`
`{ ( f '(x) = 1, x >= 0), ( f '(x) = -1, x <= 0 ) :}`
`"So we see there is a discontinuity in x=0 for f '(x)."`
`"For the rest, it is differentiable everywhere."`