9.6 Tangent Planes and Normal Lines
INTRODUCTION
The notion of the gradient of a function of two or more variables was introduced in the preceding section as an aid in computing directional derivatives. In this section we give a geometric interpretation of the gradient vector.
Geometric Interpretation of the Gradient—Functions of Two Variables
Suppose f(x, y) = c is the level curve of the differentiable function z = f(x, y) that passes through a specified point P(x0, y0); that is, f(x0, y0) = c. If this level curve is parameterized by the differentiable functions
x = g(t), y = h(t) such that x0 = g(t0), y0 = h(t0),
then the derivative of
Get Advanced Engineering Mathematics, 7th Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
