Question

The value of k such that $f\left(x\right)=x^k$ is $(n-1)$ times differentiable at 0 but not $n$ times differentiable at 0 is

• A. $\frac{2n-3}{3}$
• B. $\frac{3n-2}{3}$
• C. $\frac{4n-3}{3}$
• D. None of these

Answer 1

The correct option is B $\frac{3n-2}{3}$

The value of k for which
the function $f\left(x\right)=x^k$ is n-1 times differentiable at 0 but not n times
differentiable at 0 should be less than n and greater than n-1 .

Hence, option B is correct.