What is the geometric significance of differentiable vs continuously differentiable for functions (based on $\mathbb{R}$)? By 'geometric' i mean the appearance of the plot of such functions.
Perhaps this question is best splilt into three categories: $\mathbb{R}$ to $\mathbb{R}^n$, $\mathbb{R}^n$ to $\mathbb{R}$, and $\mathbb{R}^n$ to $\mathbb{R}^m$.
