Question

Which of the following functions is continuous but not differentiable at x = 1?

Functions:

I.y=3√x-1

II.y={x^2,x≤1
2x,x>1
III. y={x,x≤1
1/x,x>1

I'm not really sure how to do this, but I've been trying and I keep getting

both I and III.. am I wrong?

Answer 1

I is neither continuous nor differentiable
f(x) does not exist for x<1, so there is no limit from the left.
Taking just the limit on the right, y' does not exist at x=1.

II is not continuous, so cannot be differentiable
y(1) = 1
lim x->1+ = 2

III is continuous, bit not differentiable.
y'=1 for x <=1
y' -> -1 as x->1+

Answer 2

On apex 1 and 3 are both correct
so select the option 1 and 3 only