This is insane JEE Question, let's see how many here can even approach it, Challange:
If f(x) is a differentiable function and g(x) is a double differentiable function such that |f(x)|ā¤1 and f'(x)=g(x). If f^2(0)+g^2(0)=9. Prove that there exists some cā(ā3,3)such that g(c).g''(c)<0.