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Let f(x) be differentiable function and ...

Let `f(x)` be differentiable function and `g(x)` be twice differentiable function. Zeros of `f(x),g^(prime)(x)` be a,b respectively, `(a < b)`. Show that there exists at least one root of equation `f^(prime)(x)g^(prime)(x)+f(x)g(x)=0` on `(a , b)`.

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