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.

Question

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.

tkhunny · Answer

You probably should evaluate:

f(0), f(1), f(2), f(3), f(4), f(5), and f(6) and ponder the results.