Question

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x,y) - 2x2 - 6x + 6xy2 local maximum value(s) local minimum value(s) saddle points) Need Help? Read it Talk to a Tutor Submit Answer (-/3 points) DETAILS SCALCET8 14.7.014. MY NOTES PRACTICE ANOTHER Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = 6y cos(x), OS X5 27 local maximum value(s) local minimum value(s) saddle point(s) (x, y) = Need Help? Read It Talk to a Tutor (-/3 Points] DETAILS SCALCET8 14.7.015. MY NOTES PRACTICE ANOTHER Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) - 4e cos(y) local maximum value(s) local minimum value(s) saddle point(s) (x,y) = Need Help? Read It Watch It Talk to a Tutor (-/3 Points] DETAILS SCALCET8 14.7.019. MY NOTES PRACTICE ANOTHER Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = y2 - 10y cos(x), -15x57 local maximum value(5) local minimum value(s) saddle point(5) (x, y, f) =

Answer 1

o 2. solution : Given that finly) = 2x² but Guy? fm = 64²- 6 + 6y2 fy = lany Putting fu = fy=0 6(m2-1 +42) = 0 Ż n² + y2 = 1 6 7 Z and lang O nei know = 21 that ca+y² u²+ y² + any ² (a ty)² = 1 + 0 7nty so the critical points arce (1,0), (-1,0), (0,1),(0,-1) and from = 124 fyy fuy = 124 Bo 122, 2 que fan fyy fuy (1,0 = (rang-lay - 14442 =D1(1,0) fan lio 144 yo = 12 yo (1:0) (1:0) 1444²_14492 and fun and fun 70 at (160) ... The point (1,0) is a local minimum. Since pro CS Scanned with CamScanner

2 (-1,0) a local maximum At (-1,0) fun 1 (-1,0) =-12 TO = 144 (72-72) = 144 (12-0) = 144 70 Since Dyo and from To at (-1,01 " The point (-1,0) is At (0,1) fan ( 10.1 이 (44 (42-43) (0:1) 144(0-1) = -144 so Since DTO then (0,1) is a saddle point 4 (0,-1)! O fun Icon) ple 01-1) 144 (4299 144(0-1) = -144 20 Since. DTO, then (0-1) is a saddle point. ( Local maximum = -, o, f(-1,0)) - (-1,0,4) = (1,0, F11,0)) = (1,0, -4) Saddle points = ((only fron), (0,-1, f(0-1)) horal (Yinimum 0 ( 0 CS Scanned with CamScannet