The oracle function f(x,y) is presented below. For each point (x,y) you enter the oracle will tell you the value f(x,y). Estimate the partial derivative of the function at (1.6,−0.0999999999999999) using the Newton quotient definition.

3 answers

you need a difference. if you are looking at the given point, try these points into the oracle x=1.59, and x=1.61 (h=.02), and you now have f(x+h), and f(x)
then it will give you f(x) at those points, then do this https://www.youtube.com/watch?v=1O5NEI8UuHM
Suppose you want ∂f/∂y
We can approximate that by
(f(x,y+h)-f(x,y)) / h
So just plug and chug. For ease of typing, I'll use (1.6,-0.099)
You can add as many zeroes as you want.
(f(1.6,-.1+0.001)-f(1.6,-0.1))/0.001
You have not said what f(1.6,-0.1) is, so that's all I can say at the moment.
I just did that exercise on my webwork assignment, do the following:

1) Calculate in the oracle f in the point 1 they gave you (1.6,−0.0999999999999999). Let's call this result f(x1,y1).

2) Calculate in the oracle f in a point slightly superior in the x axis. For example (1.601,−0.0999999999999999). Let's call this result f(x2,y1).

3) Use the Newton's quotient definition:
Fx (x1,y1,) = ( f(x2,y1) - f(x1,y1) ) / (x2-x1)

Where x2 is 1.601 and x1 = 1.6.

Be happy :)