Question

Question 5. (15 pts) Find the maximum and minimum of S(,y) 22 + y2 = 1. on the circle

Answer 1

Question - 2 f(x,y) xyz The points lie on x² + y2-2 => y² =1-x². f(x, y) = xey² *(1-x2) => f(x, y) x– x3 For maximum and minimum, f'(x,y) = 0 ice. a f(x, y) 0 ds d (x– x3) dx => 1 - 322 co In 32? =1 22 = I to Now, d² f(x,y) d (1-322?) -626. = - dre² da At x = d² dan f(x,y) = [-68] wit 153 -6. 3 6.7 <0. x 33 At xa st so, f(x, y) has maximum at th d? f(,y) = [- 62) - -6.6-ts) > 0 so, f(x,y) has minimum at one st

2 when n = 1-x² - wit 1- ſ = Ķ 2 2 x = -5, y = 1- * 1-I 23 3 3 Maximum value of flary) xy²=(1/3) - 6) 2 23 - = 313 9 minimum value of flay) = xy² = VE I. 2V 3 dim = و