Section 2

Question 1

Gradient of f

Answer 1

Sometimes “grad f.” grad f = del f / del x, del f / del y, del f / del z

Question 2

Tangent Plane

Answer 2

z = f(x0, y0) + del f(x0, y0)(x - x0) + del y(x0, y0)(y - y0)
where the original surface is z = f(x, y) and the point the plane is tangent to is (x0, y0)

Question 3

Near the point (x0, y0), can y be expressed by a function of x?

Answer 3

If del f / del y at (x0, y0), does not equal zero, then there is a function of x that represents y near (x0, y0).