Use the Intermediate Value Theorem to show that at least one

Use the Intermediate Value Theorem to show that at least one zero lies in the given interval for the given polynomial. f (x) = x^3 - 6x + 1, between x = 2 and x = 3 Substitute x = 2 and x = 3 into the function and simplify. f (2) = f (3) = Interpret the results using the Intermediate Value Theorem. Because f is a polynomial function and since f (2) it and f (3) is, there is at least one real zero between x = 2 and x =

Solution

Solution:

at least one zero in between x =2 and x =3

f(x) = x^3 -6x +1

f(2) = 2^3 -6*2 +1 = -3

and

f(3) = 3^3 -6*3+1 = 10

and

since f(2) is below and f(3) is above , there is at least one real zero between x =2 and x =3