Tuesday, 3 May 2016

derivatives - Real Analysis. Suggestions.





Let f,g:[a,b]R continuous in [a,b] and differentiable in (a,b) such that f(a)=f(b)=0, then, theres exist c(a,b) such that:
g(c)f(c)+f(c)=0.




I tried to use the Rolle's Theorem and Means Value Theorem, but I couldn't define an auxiliary function φ to help me. I didn't want a solution of exercise, just a suggestion.


Answer



Use φ(x)=f(x)eg(x)


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