Thank you for the opportunity to help you with your question!
Since f(x) is a polynomial function, I'm going to present a simple way of finding the the value(s) c where f is continuous.
All polynomial functions that are sums powers of x are everywhere differentiable everywhere: that is, for all values on the real line. If a function is differentiable at x, it is also continuous at x.
Since f(x) is differentiable everywhere, it is continuous everywhere. That is f(x) is continuous for every value of x: hence for every c in (-infinity,+infinity).
If you haven't had differentiation yet, post the problem again and specify that the solution can't use the property of differentiability..
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