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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2017 · Mathematics · Continuity and Differentiability

Suppose the function f(x)= ^ n , n ≠ 0 is differentiable for all x...

Suppose the function f(x)=\mathrmxn,n≠0f(\mathrm{x})=\mathrmx^{\mathrm{n}}, \mathrm{n} \neq 0 is differentiable for all xx. Then nn can be any element of the interval

Options

  1. A(1,∞)(1, \infty)
  2. B(0,∞)(0, \infty)
  3. C(12,∞)\left(\frac{1}{2}, \infty\right)
  4. DNone of the above

Correct answer

A. (1,∞)(1, \infty)

Step-by-step solution

f(x)=xn,n≠0f(x)=x^n, n \neq 0 This function is differentiable for all values of nn, except 0. Hence n∈(1,∞)n \in(1, \infty)
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