2. f(x) = 3x^3 - 6x^2 + 3x + 6
Here's the graph : https://www.desmos.com/calculator/68wqsc5sft
Possible positive roots .. f(x) has two sign changes so two or zero possible positive roots
f(-x) = -3x^3 - 6x^2 - 3x + 6 = 1 sign change so one or zero posiible negative roots
Rational Roots Theorem shows that the possible rational roots are ± [ 1/3, 2/3, 1, 2, 3, 6 ]
Upper Bound
2 [ 3 -6 3 6 ] 3 [ 3 -6 3 6 ]
6 0 6 9 9 36
______________ ________________
3 0 3 12 3 3 12 42
All the signs on the bottom row are positive whne x = 3.....so this is the upper bound on zeroes
Lower Bound
-1 [ 3 -6 3 6 ]
-3 9 -12
______________
3 -9 12 -6
We have alternating signs on the bottom row.....therefore....x =-1 is the lower bound on zeroes
The y intercept is (0,6)
The x intercept (and the only real root) is x ≈ -.696
