However, $f(x)$ is not continuously differentiable at $x=0$ since $f'(x)$ does not exist for $x \neq 0$ or is not continuous at $x=0$ in a certain sense;
Final note: If you are looking for a gentle introduction to calculus, buy Stewart. If you want to become a mathematician, buy Demidovich. And buy a lot of pencils. You’re going to need them. demidovich calculus
Covers everything from limits and single-variable calculus to multiple integrals, field theory, and differential equations. Internet Archive 🗂️ Core Topics Covered However, $f(x)$ is not continuously differentiable at $x=0$
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