# Need help in determing gradient of this function?

• Mar 6th 2010, 03:17 AM
eriiin
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.

• Mar 6th 2010, 04:06 AM
Prove It
Quote:

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.

First of all, what do your $x$ and $y$ represent?
• Mar 6th 2010, 04:08 AM
eriiin
x represents the day of the year and y represents the length of the day (sunrise to sunset) in minutes.
• Mar 6th 2010, 04:11 AM
Prove It
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 $x$.

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