Assignment:
Q1. A function f:(a,b)->R is increasing on (a,b) if f(x)<=f(y) whenever x=0 for all x belong to (a,b).
Q2. Show that the function g(x){x/(2+x^2 sin(1/x)) if x not=0 0 if x=0 is differentiable on R and satisfies g'(0)>0. Now prove that g is not increasing over any open interval containing 0.
Provide complete and step by step solution for the question and show calculations and use formulas.