Clever PROOF Function is CONSTANT using Calculus!
We prove that if a function f from the real numbers to itself satisfies a certain inequality, then it must be a constant function. The beautiful thing about this proof is that it uses theoretical calculus to solve a problem that makes no direct reference to calculus. The video will be important for mastering math proofs and rigorous mathematical thinking for people studying calculus and real analysis. In the proof, we also appeal to important theorems and ideas on limits and differentiation, such as difference quotients and the limit definition of the derivative, the sandwich theorem (or squeeze theorem) for limits, and the mean value theorem for differentiation.
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