Consider the function f(x)=2x^3+4x^2+3, and let c be a number in the interval [0,1]. For what values of k is there a c in the interval such that ?
Since f is a polynomial, it is continuous in the interval [0,1].
f(0) = 3
f(1) = 9
Therefore, for every value of k in the interval [3,9] there is a c in the interval [0,1] such that .