In colder climates the cost for natural gas to heat homes can vary from one month to the next. The polynomial function given by f(x) = -0.1213x⁴ + 3.462x³ - 29.22x² +64.68x + 97.69 models the monthly cost in dollars of heating a typical home. The input x represents the month, where x = 1 corresponds to January and x = 12 to December. 

(a) Where might the absolute extrema occur for 1≤ x ≤ 12? 

(b) Graph  in [1, 12, 1] by [0, 150, 10]. Find the absolute extrema and interpret the results.