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Assume that ψ : [a, b] → R is continuously differentiable. A critical point of ψ is...

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Advance Math

Assume that ψ : [a, b] → R is continuously differentiable. Acritical point of
ψ is an x such that ψ'(x) = 0. A critical value is a number y suchthat for at
least one critical point x we have y = ψ(x).
(a) Prove that the set of critical values is a zero set. (This isthe Morse-Sard
Theorem in dimension one.)
(b) Generalize this to continuously differentiable functions R →R.

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