07Adiffconditions

= Conditions of Differentiability =

The derivative is only defined if the function is __continuous__ and __smooth__.

This means the derivative does not exist (is not defined) in the following conditions:
 * where there is a vertical asymptote
 * where there is a break or a hole
 * where there is a sharp corner (cusp)
 * at the endpoints of the domain




 * f '(x) is undefined at x = 1 and at x = 3
 * Because of the cusps ("pointy bits"), f(x) is not smooth at those two points




 * g'(x) is undefined at x = 1
 * Because of the endpoint
 * g'(x) is undefined for x < 1
 * Because g(x) is undefined for those values
 * g'(x) is undefined at x = 3.5
 * Because of the hole (discontinuity)

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 * h'(x) is undefined at x = 2
 * Because h(x) is undefined at the asymptote

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