# Thread: Calculus of exponentials and trip fcns: temp can be modeled by 𝑦 = 5𝑐𝑜𝑠 𝑥^2 + 25

1. ## Calculus of exponentials and trip fcns: temp can be modeled by 𝑦 = 5𝑐𝑜𝑠 𝑥^2 + 25

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?

2. Originally Posted by sampang
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?

First, I think your title should refer to trig functions, not trip functions.

Second, I would initially guess that "𝑦 = 5𝑐𝑜𝑠 𝑥2 + 25" is supposed to be "𝑦 = 5𝑐𝑜𝑠 𝑥2 + 25", and "𝑑𝑑𝑥cos𝑥2 = −12sin𝑥2" should be "𝑑/𝑑𝑥 (cos𝑥2) = −12sin𝑥2".

But -- that isn't true! So my guess has to be wrong. Maybe it was really "𝑦 = 5𝑐𝑜𝑠(𝑥/2) + 25" and "𝑑/𝑑𝑥(cos(𝑥/2)) = −12sin(𝑥/2)". But that isn't right, either.

Finally, you haven't stated whether the formula assumes the cosine takes degrees, radians, or something else. That is important contextual information.

Please make sure that you copied the problem exactly. What you appear to have done is to paste from some electronic source for which copying loses part of the formatting. By not even checking what you pasted in, you have shown that you have put in no effort at all, which is not a good way to start when you ask for help.