A differentiable manifold class $C^k$ but not class $C^{k+1}$

Question

Please show that the graph of $f(x)=|x|^λ$, where $k<λ<k+1$ is a differentiable manifold of class $C^k$ but not class $C^{k+1}$. (Problem in Differential Topology, Hirsch, Morris W.) Or, please show other examples.