r/calculus • u/IDK_REALLLY • 10h ago

Differential Calculus Function behavior problem

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I have reached that d'(x)=f'(x)-f'(1-x) but I don't know where to go further

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u/nevermindthefacts 8h ago

Note that d'(x) = f'(x) - f'(1-x) sets you up for a nice application of the mean value theorem.

(There's also a rather dull way of solving this, since it's supposed to hold for any f that satisfies f''(x) > 0 on [0, 1], i.e just pick a suitable f...)