Differentiability

Question

Comments

x^2 is twice differentiable.

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But a>1 also includes a=1.5

Answer must be a>=2

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maybe this is incomplete question, they must say that a belongs to N or R
but generally power attain interger so, closest option would be D

Answer 1

Twice Differentiable: It means that it second derivative is defined for all input values within it’s range.

For example see the function

f(x)=x|x| , with

f ′ (x)=|x| 

f ′′ (x)   is undefined for x=0, thus f ′ (x) is not differentiable.

f(x)  is differentiable, but not twice differentiable.

To know how to check differentiability of a function: https://www.mathsisfun.com/calculus/differentiable.html

In the above question assuming a ∊ N, then the Correct Answer is D.  i.e. f(x)=x².