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Suppose the function f(x) = xn, n ≠ 0 is differentiable for all x. Then n can be any element of the interval

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  1. [1, ∞)
  2. (0, ∞)
  3. \(\left( {\frac{1}{2},{\rm{\;}}\infty } \right)\)
  4. None of the above

Answer (Detailed Solution Below)

Option 1 : [1, ∞)
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Detailed Solution

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Calculation:

Given: f(x) = xn, n ≠ 0.

F’(x) = nxn – 1

For f(x) to be differentiable for all values of x, n – 1 ≥ 0

So, n ≥ 1.

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