Show that f(x) = x2 is differentiable in 0 <x<2.
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Answer:
Let a function f(x)=x
2
Now, for differentiability at x=0
f(x)={
0,x=0
x
2
,x
=0
h→0
lim
[
h
f(h)−f(0)
]=
h→0
lim
h
f(h)
Right limit is
h→0
+
lim
h
f(h)
=
h→0
lim
h=0
Left limit is
h→0
−
lim
h
f(h)
=0
Since, R.H.L=L.H.L
and limit is also exist so f(x)=x
2
is differentiable at x=0.
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