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Lower and upper bounds for a given function are important in manymathematical and engineering contexts, where they often serve as a base forboth analysis and application. In this short paper, we derive piecewise linearand quadratic bounds that are stated in terms of the Lipschitz constants of thefunction and the Lipschitz constants of its partial derivatives, and serve tobound the function's evolution over a compact set. While the results followfrom basic mathematical principles and are certainly not new, we present themas they are, from our experience, very difficult to find explicitly either inthe literature or in most analysis textbooks.

On linear and quadratic Lipschitz bounds for twice continuously differentiable functions