01 Recall ordinary derivatives If y is a function of x then dy dx is the derivative meaning the gradient (slope of the graph) or the rate of change with respect to x 02 Functions of 2Example Consider the function f(x;y) = 4 1 4 (x 2 y2) To understand the graph of z= f(x;y), we can study trace curves The vertical trace curves are curves made by intersecting the graph with planes of either constant xor y Clearly, if y= kis constant, the equation z= 4 1 4 (x 2 k2) gives a downward opening parabola147 Maxima and minima Suppose a surface given by f ( x, y) has a local maximum at ( x 0, y 0, z 0);
Differentiating Related Functions Intro Video Khan Academy
