Question

if f(x)=x^3-x^2+x show that there is a number c such that f(c)=10

Answer 1

range of cubic function is always all real numbers, so it is true for any \(c\)

Answer 2

or rather any \(f(c)\) is what meant
in other words, given any \(a\in \mathbb{R}\) there is some \(x\)for which \(f(x)=a\) as \(f\) is a polynomial of degree 3

Answer 3

@Eid the simple way is to find its maximum and minimum value as the function is continuous (polynomial function) so if 10 lies in it then it is true otherwise false:)