Continuity and Differentiability of root mod function

Question

1) Consider f(x) =  $|x|^{3/2}$ Check for Differentiability and Continuity. I am getting Cont and Differentiable both.

2) Consider f(x) =  $|x-1|^{3/2}$ Check for Differentiability and Continuity. I am getting Cont and Differentiable both.

3) Find the value of  $f(x) = \int_{-2}^{2}|1-x^4|dx$. I am getting 8/5, but answer is 12.

Comments

for 3rd link

for 1st and 2nd you forget to give limit .

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It is the simple function like we have |x| which is continuous over all values on the number line but not differentiable at x = 0.

Answer 1

give function is f(X) is continuous and not differentiable.

 $f(x)=\left\{\begin{matrix} x^{3/2} ,x>=0 & \\-x^{3/2} ,x<0 & \end{matrix}\right.$
f(0)=0.

LHL and RHL.

lim x->(0-) = limx->(0+)=f(a)= 0.

since, LHL = RHL =f(a).
 the limit exist and the given funtion is continious.

and |x|^3/2 is not diffrentiable as  LHD ¥ RHD.