(4A-1)   This curve is the intersection of the function z = x2 +  2y2 with the plane x = -0.5.


①   substituting in the fixed value of x, we get:  z = 0.25 + 2y

②  Differentiating, we get:     dz/dy = 4y.  So at y = -0.5:   dz/dy = -2

This is the gradient of the tangent.

③  z = x2 +  2y2, so ∂z/∂y = 4y. This is the same as we got in ② because the partial derivative is defined as the derivative with respect to y when x is constant, which is - obviously - the case when we define x = -0.5