I need to know which of the appropriate axioms and theorems and which method of proof you may use (e.

Can someone help me understand this problem. I need to know which of the appropriate axioms and theorems and which method of proof you may use (e.g., direct proof, proof by construction, proof by contradiction, proof by induction, etc.). for answering this problem.

Exercise 4.4.5. Let F:R->R be a function. Suppose that f is differentiable, that f(0)=1 and that |f'(x)| less than or equal to 1 for all x E R. Prove that |f(x)| less than or equal to |x|+1 for all x E R.

I'm also trying to understand how to do the problem. It has been awhile since I've done differentiable problems.