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..

Please let me know if you need any clarification. I'm always happy to answer your questions.