3.The weather in a given country can be modelled approximately by the curve 𝑦 = 5𝑐𝑜𝑠 𝑥2 + 25.

x is the number of the month (e.g. March is 3) and y is the average monthly temperature.

(a) Using transformations of graphs, explain why 𝑑𝑑𝑥cos𝑥2= −12sin𝑥2

(b) Using calculus, determine which month is the hottest.

(c) During which months is the temperature increasing?

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