Thread: Need help in determing gradient of this function?

I am trying to determine what day of the year the length of the day is increasing the most rapidly. I have collected the data, modelled a graph and acquired the function: y=155.5*cos1.1457x + 1182.8

I understand that the length of the day increasing the most will be when the gradient will be at it's highest, but I don't know what to do once I've gotten the equation.

Please help (:

Originally Posted by eriiin

I am trying to determine what day of the year the length of the day is increasing the most rapidly. I have collected the data, modelled a graph and acquired the function: y=155.5*cos1.1457x + 1182.8

I understand that the length of the day increasing the most will be when the gradient will be at it's highest, but I don't know what to do once I've gotten the equation.

Please help (:

First of all, what do your $\displaystyle x$ and $\displaystyle y$ represent?

x represents the day of the year and y represents the length of the day (sunrise to sunset) in minutes.

If you take the derivative of this function, you get the rate at which the length of the day is increasing or decreasing.

But you want the maximum increase.

So you will need to differentiate this derivative again (i.e. find the second derivative), set it equal to 0, solve for $\displaystyle x$.

You will then need to use an appropriate test to verify which values you have found are maximums.