Problem 53E

Graphing Equations

Use the steps of the graphing procedure on page 248 to graph the equations. Include the coordinates of any local and absolute extreme points and inflection points.

MATH 2450 WEEK 7 Strategy On a close domain, look for all critical points inside the domain. Look for the boundary points then compare. Look for all critical points inside the domain: F = 0 x Fy= 0 Look for all critical points on the boundary g’(t) = 0 Look at the boundary points of the boundary EX. Find the absolute max/min f(x,y) = e(2) - over the disk x + y <= 1 1) x + y < 1 2) x + y = 1 x^(2) - y^(2) Fx= 0 2xe = 0 x = 0 x^(2) - y^(2) Fy= 0 -2ye = 0 y = 0 Po= (0,0) Forms of absolute minimum and maximum 1) Y = sqrt(1-x ) -1<= x <= 1 Y = -sqrt