Is a bijective continuous function:[a,b]->[f(a),f(b)] differentiable?(adsbygoogle = window.adsbygoogle || []).push({});

I think it has to be.

continuity between two distinct values of f(a) and f(b): it gotta take all the values between f(a) and f(b) at x in [a,b], by the intermediate value theorem.

if f is bijective, at [a,b], f(x) can't go up and then down at [a,b]. it has to be monotonically increasing for it to be bijective.

so a function can only be non-differentiable at a set of points of measure zero. (like the vertical tangent of f(x)=x^1/3 at 0)

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# Bijective & continuous -> differentiable?

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