CONTOUR PLOT AND LEVEL CURVES 1 2 y 1 2 10 x 2 y 2 2 y 2 - PDF document

CONTOUR PLOT AND LEVEL CURVES − 1 2 − y  1  2 − 10  x 2 − y 2 2 − y 2 The " peak " function: z = 3  1 − x  2 e − x 5 − x 3 − y 5  e − x 3 e − x  1  CAN YOU IDENTIFY THE LOCAL MAXIMA AND MINIMA BY LOOKING AT THE LEVEL CURVES? HOW ABOUT THE SADDLE POINTS? 1 5 1 0 5 0 2 3 2 0 1 0 - 1 - 2 - 2 - 3 y x

Answer: x ≈ 1.28 , y ≈− 0.0048 Local Maximum x ≈ .228 , y ≈− 1.625 Local minimum x ≈− .460 , y ≈− .629 Local Maximum x ≈− 1.35 , y ≈ .204 Local minimum x ≈− 0.01 , y ≈ 1.58 Local Maximum x ≈ .296 , y ≈ .320 Local minimum x ≈− .266 , y ≈ .467 Saddle point x ≈ .416 , y ≈− .394 Saddle point x ≈ 1.10 , y ≈ .854 Saddle point Below, "m" stands for local minimum, "M" stands for local maximum and "S" stands for Saddle point.