LimitsHard
Question
If f(x) = x
, then indicate the correct alternative(s):
, then indicate the correct alternative(s):Options
A.f(x) is continuous but not differentiable at x = 0
B.f(x) is differentiable at x = 0
C.f(x) is not differentiable at x = 0
D.none
Solution
f(x) = x
is continuous at x = 0
f′(x) = x
+ x 
f′(x) =
f′(0+) f′(0-) = - 1
Hence it is differentiable at x = 0
is continuous at x = 0 f′(x) = x
+ x f′(x) =
f′(0+) f′(0-) = - 1
Hence it is differentiable at x = 0
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