Laboratory on Derivatives and Cross Sections

Problem #1

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

1. Which variable remains constant if we speak of and what will the constant value of that function be if we wish to find f_x (0, 1).
   
   
2. Substitute the constant value obtained in (1) into f and place the associated cross section over your 3D Kit. (Note, use 2 notches for 1 unit in x and y and 1 notch for 1 unit in z).
   
   
3. Place the tangent line of this cross section that points in the x direction and starts at the point (0, 1) in your kit. Approximate the slope of this tangent line by finding the rise and run on your kit.
   
   
4. Use the formula for the cross section to obtain the precise value for the slope of the tangent line in the cross section at the point (0, 1).
   
   

Problem #2

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

1. Which variable remains constant if we speak of and what will the constant value of that function be if we wish to find f_y (1, 0.5).
   
   
2. Substitute the constant value obtained in (1) into f and place the associated cross section over your 3D Kit. (Note, use 2 notches for 1 unit in x and y and 1 notch for 1 unit in z).
   
   
3. Place the tangent line of this cross section that points in the y direction and starts at the point (1, 0.5) in your kit. Approximate the slope of this tangent line by finding the rise and run on your kit.
   
   
4. Use the formula bar for the cross section to obtain the precise value for the slope of the tangent line of the cross section at the point (1, 0.5).