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Hi:) I have a couple of questions regarding the interval value theorem. Using the intermediate value theorem, show that the polynomial f(x) = x^3 -

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!

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