Quite simple. Just to make you relaxed !

Calculus Level 5

Let $f:\mathbb{N} \to \mathbb{N}$ be an identical function w.r.t $x$ . Find $f'(x).$

None of the given choices.

\dfrac{x^2}{2}

x

-1 0

1 solution

Sandeep Bhardwaj
May 30, 2015

Since $f$ is defined over $\mathbb{N}$ $\implies$ $f$ is discrete function.

So $f$ is not continuous function over real $x.$

And any function which is not continuous can never be differentiable.

Hence $f'(x)$ doesn't exist which is not given in the options. Hence "None of the given choices" is correct answer.

Ohh!! You got caught. Don't mind, try more problems of mine. :P

enjoy !

Be careful though, in some cases, if a function is defined on the integers, then the derivative is understood as the finite difference.

i did'nt understand, can you help , sir ? why is it undefined,plz explain , i'm not an intelligent boy ! :(

A Former Brilliant Member - 4 years, 5 months ago

what is an identical function ?

A Former Brilliant Member - 4 years, 5 months ago