please help me with these problems?

The goal of this problem is to show that the function f(x) = x^{3}-9x^{2}+23x-13 has three distinct roots in the interval [0, 6]. Use the Intermediate Value Theorem to list three distinct open intervals in [0, 6], where each interval contains a root of ,f(x) and has the form (a, a+1), where a represents an integer. 2) The Intermediate Value Theorem may be used to show that there is at least one solution of the equation 5cos(3 x) + x^2 = sin(3 x) for x [0, pi]. To do this, we define the function f(x) = 5cos(3x)+x^{2}-sin(3x). f(x) is continuous for [0,pi] a) Enter the coordinates of a point (x, y = f(x)) with a positive y-coordinate b) Enter the coordinates of a point (x, y = f(x)) with a negative y-coordinate