zz = f(x,y)x(^0) y
Tangent plane
Figure 16.3The tangent plane.
of the slope and rate of change of the surface at the point of tangency (Figure 16.3 – think
of the mortar-board you may one day be wearing!).
Any line in the tangent plane is also tangent to the surface. In particular, the lines
parallel to thexzandyzplanes – the slopes of these lines give the slope of the surface
in thex-direction andy-direction respectively.
Exercise 16.2
Sketch the surface representing the function
z=x^2 +y^2
Answer
z
y
z = x^2 +y^2 = 2
x
1
02
1
Figure 16.4