Question

Given the polynomial f(x) = 3x ^ 3 - 4x ^ 2 - 3x - 1 what is the smallest positive integer a the Intermediate Value Theorem guarantees a zero exists between 0 and a? Enter an integer as your answer . For example , if you found a = 8 you would enter 8. Provide your answer below .

Answer 1

9514 1404 393

Answer:

2

Explanation:

You need the smallest positive integer for which f(x) > 0.

f(1) = 3 -4 -3 -1 = -5

f(2) = ((3·2 -4)2 -3)2 -1 = (4 -3)2 -1 = 1

x = 2 is the smallest integer for which f(x) > 0.