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Find all functions

Source: MTRP 2019 Class 11-Short Answer Type Problems: Problem 1 :-

April 9, 2020

function

Problem Statement

Find all functions

f:\mathbb{R} \to \mathbb{R}

such that

f(x)\geq 0\ \forall \ x\in \mathbb{R}

f'(x)

exists

\forall \ x\in \mathbb{R}

and

f'(x)\geq 0\ \forall \ x\in \mathbb{R}

and

f(n)=0\ \forall \ n\in \mathbb{Z}