I am struggling with this problem I have to use calculus to find an expression for the rate of change of temperature with respect to time;
T = 25 - 4cos((π(t-3))/12)
This is the equation in which I need to differentiate. I haven't differentiated sine or cosine functions before?
*note that π is supposed to be pi = 3.142
If anybody could help me, your help is mostly appreciated
For that equation, the y-value is the same (it is always -0.5236)
When typed into a graphics calculator, the equation is just a constant line?
In the question, it says that 'whenever the rate of change of temperature, with respect to time, is greater than or equal to +0.2(degrees Celsius) per hour, the system switches on. It switches off again when the rate of change of temperature, with respect to time is less than +0.2(degrees Celsius) per hour.
Hence find the range of values of t (correct to two decimal places) for which the watering system will be on.
Shouldn't the derivative be oscillating?