(c) The Second Derivative Test fails for points on the unit circle (this can be checked by some lengthy algebra). Prove, however, that f takes on it maximum value on the unit circle by analyzing the function g() = te 35. f(x for t > 0. 36. f( 27. CAS Use a computer algebra system to find a numerical approxi. mation to the critical point of f (x, y ) = ( 1 -x+x2)e" + ( 1 - y + > > > e * ? Apply the Second Derivative Test to confirm that it corresponds to a local minimum as in Figure 21. FIGURE 21 Plot of f (x, y) = (1-x+x2)ex-+(1-y+>2)ex. 28. Which of the following domains are closed and which are bounded? (a) { (x, y) E R2 : x2 + 12 = 1} (b) { ( x, y ) E R2 : x2 + 12 0, y > 0} (e) { (x, y) ER2 : 1 5 x 5 4, 5 s y s 10} (f) { (x, y) ER2 : x > 0, x2 + 12 = 10} In Exercises 29-32, determine the global extreme values of the func- tion on the given set without using calculus. 29. f (x, y ) = x+y, O