Not every smooth function on \(\mathbb{R}^n\) is real analytic. A counter example is a cutoff function , then the Taylors series vanishes at \(a\) and \(b\) but it does not vanish locally at these points.
Not every smooth function on \(\mathbb{R}^n\) is real analytic. A counter example is a cutoff function , then the Taylors series vanishes at \(a\) and \(b\) but it does not vanish locally at these points.