Hi:) I have a couple of questions regarding the interval value theorem.

1. Using the intermediate value theorem, show that the polynomial f(x) = x^3 - 15x + 1 has three zeros on the interval [-4,4]. (consider the values of f(x) at x = 4,3,1,0,-1,-3,-4)
2. Verify that the intermediate value theorem applies on the indicated interval of [0,3] when given f(x)=x^2 - 6x +8, and find the value of c such that f(c)=11.
3. Take the values in the table listed below of two continuous functions g(x0 and f(x):

x	-5	-2	1	2	4
f(x)	4	8	-2	-5	-7
g(x)	-1	7	-4	-3	3

Which interval is guaranteed to contain a point c such that g(c)=f(c) and why?

A) (2,4)

B) (-5,-2)

C) (-2,1)

D) (1,2)

Thank you!