In Spivak's Calculus, on page 121 there is this theorem(adsbygoogle = window.adsbygoogle || []).push({});

Then he generalizes that theorem:

I tried proving theorem 4 on my own, before looking at Spivak's proof. Thus I let c = 0 and then by theorem 1, my proof would be completed. Is this a correct proof?

Spivak's proof for theorem 4:

And also can someone explain to me the choice of why Spivak has chosen the equation g = f - c. I understand his proof but the choice would have never occurred to me intuitively.

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# I Spivak - Proof of f(x) = c on [a, b]

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