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Let f be continuous on [a,b] and differentiable on (a,b) Suppose that:

f^{2}(b) f^{2}(a) = b^{2}- a^{2}:

Prove (using Rolle's theorem) that:

( exists x belonging to (a, b) ) ( f'(x)f(x) = x )

I just don't know where to start i've done basic proofs with the theorem but only when f(a) = f(b). Any help would be greatly appreciated.

Thanks

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# Proof Using Rolle's Theorem

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