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CAL

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?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  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+

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. On apex 1 and 3 are both correct
    so select the option 1 and 3 only

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

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