Question

show that f(x) = x^2 is continuous and differentiable at x=0​

Answer 1

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.