If f(x; y; z) = z sin (xy), find the rate of change of f at the point P(0; 0; 2) in the direction from P to Q(3; 0; 0)

(b) In what direction does f have the maximum rate of change? What is the

maximum rate of change?

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is