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

Assume that ψ : [a, b] → R is continuously differentiable. A critical point of
ψ is an x such that ψ'(x) = 0. A critical value is a number y such that 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 is the Morse-Sard
Theorem in dimension one.)
(b) Generalize this to continuously differentiable functions R → R.

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Expert Solution

Colby Messinger answered 1 year ago

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