Laboratory on the Definition of Derivatives

Problem #1

The function f is represented by the formula f (x, y) = 2x² + y² + 1.

1. Fill the following table to approximate
   
   

   Run	Rise	slope
   2
   1
   .5
   .1

   
   
   
2. From this table, what would you guess is the value of ?
   
   
3. Fill in the following table to approximate
   
   

   Run	Rise	slope
   2
   1
   .5
   .1

   
   
   
4. From this table, what would you guess is the value of ?
   
   
5. Fill in the following table to approximate to obtain the derivative in the direction NE along the line y = x.
   
   

   Run	Rise	slope
   2
   1
   .5
   .1

   
   
   
6. From this table, what would you guess is the value of the derivative in the NE direction?