Q 1,3,4,5) Since it is a polynomial with odd degree with positive leading coefficient so the upper bound is positive infinity and lower bound is negative infinity.
2) 2x4 – 3x3 + 6x2 + 2x + 16
first derivative of the polynomial is 8x3 - 9x2 +12x +2
The minimum is when first derivative is 0.
So, 8x3 - 9x2 +12x +2 = 0
x = -0.148 (approx) using Newton-Raphson method, if you wish to know how I came up with it, post a new question.
2nd derivative test to confirm that is really a minima.
derivative of 8x3 - 9x2 +12x +2 is 24x2 -18x +12
when x = -0.148 then 24x2 -18x +12 > 0
So the lower bound is when x = -0.148 approx
and upper bound is positive infinity, since it is an even degree polynomial with positive coefficien.