Zeros of functions with nonvanishing second derivative and the roots of $x^2-\sin x$

Suppose \(f\) is continuous on \([ a , b ]\) , twice differentiable on \(( a , b )\) , and \(f ^ { \prime \prime } ( x ) \neq 0\) for all \(x \in ( a , b )\) Prove carefully that \(f\) has at most 2 distinct zeros in \([ a , b ]\)

Prove that the function \(f ( x ) = x ^ { 2 } -\) sin x has precisely two roots.