Problem in Partial Derivatives and Gradient Quiz

Course Q&A Math for Machine Learning Calculus for Machine Learning and Data Science
1

In problem 3 it asks to find the minimum value given a set of functions but If I give a value it said it should be a point. If I give a point them it says it is not a number. It also says to check the gradients notation which it just return me to coursera main page. Could anyone help me to understand what is the format the quiz wants me to answer to that question?

2

If it’s the same problem that I’m seeing, then it’s asking for the minimum value of f(x,y), which would be just a single number. If you have the (x,y) point at which f(x,y) would be at its minimum, then you’d need to plug in the x and y values that you have in order to come up with f(x,y) at that point.

3

Dear Octavio,

Thanks for your post. Please find my comments:

  1. It is possible that the question are not in the same order. Consequently, it would be good to know the specific questions you are having issues with. In my case, by following your description if I goes to problem 3, then the proposed question is asking me to find the df/dy for a given function which is different to what you are describing.
  2. However, problem 4 is asking me to find the minimum value of the function f(x,y)=2x^2+3y^2-2xy-10*x
    Which I believe is the question you are having issues with.

In this case, you need to take the following approach:
a. Remember that to find a minima/maxima you need to find the points in the function where the derivates are equal to 0.
b. Because this is a function with multiple variables you need to take the gradient which is nothing else that taking both derivates: df/dx, and df/dy
c. Once you have found the derivates you will end up having two equations df/dx=0, and df/dy=0.
d. Now, this is a simple system of 2 equations with 2 variables that you need to solve via either method: substitution, elimination…
e. Finally, once you have solved the system of 2 equations you will find the values of x, and y where the derivates are equal to 0. In other words, you have found the coordinates (x,y) for the minima/maxima.
g. However, the problem is asking you the value of the function not the coordinates for the maxima/minima. So, what you need to do is to replace the values of x, and y that you found in the previous step in the original equation and then do the simple math to add/subtract.
h. Bingo! You now have the answer!

I hope this help you to understand and solve the problem.

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