Exer. The average monthly temperatures in °F for two Canadian locations are listed in the following tables.
Month | Jan. | Feb. | Mar. | Apr. |
Arctic Bay | −22 | −26 | −18 | −4 |
Trout Lake | −11 | −6 | 7 | 25 |
Month | May | June | July | Aug. |
Arctic Bay | 19 | 36 | 43 | 41 |
Trout Lake | 39 | 52 | 61 | 59 |
Month | Sept. | Oct. | Nov. | Dec. |
Arctic Bay | 28 | 12 | −8 | −17 |
Trout Lake | 48 | 34 | 16 | −4 |
(a) If January 15 corresponds to x = 1, February 15 to x = 2, ..., and December 15 to x = 12, determine graphically which of the three polynomials given best models the data.
(b) Use the intermediate value theorem for polynomial functions to approximate an interval for x when an average temperature of 0°F occurs.
(c) Use your choice from part (a) to estimate x when the average temperature is 0°F.
Trout Lake temperatures
(1) f(x)= − 2.14x2 + 28.01x − 55
(2) g(x)= − 0.22x3 + 1.84x2 + 11.70x − 29.90
(3) h(x)= 0.046x4 −1.39x3 + 11.81x2 − 22.2x + 1.03
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