The problem is finding the local maximum and minimum Williams and saddle point of a function If you have three dimensional graph in software. Ralph the function whether the boy and we pointed that revealed out important as backs off the function. So first computer, half tracks. This is control. Why us, Axl? I times negative x times Each is a power connective x squared plus y squared to successfully asik Untrue. Why harms one minus X coyer times each of the power of negative I squared plus y squared over two I shall have wine a competition This is equal to X times one minus y square house needs connective exploiter a slice coyer over to you Latin Bolshevism, you called zero We have X It's the culture plus minus one. Why, you country zero war Why you could to plus or minus one I want to zero on behalf foul points plus or minus one Awesome minus one plus my swan minus plus one and zero zero. Then we computed half second Partial derivatives have x x This is the culture negative. X y hams three minus exc Lawyer How's e to the power of elective X square plus y square over to you. Why? Why This is equal to negative attacks by Pam's three Mass Life Square. How sweet is that? How often effective, exploitive plus supply squire over to you on DH X y It's in country one minus tax Coyer Times one minus y square. Sleep it off Negative exploiter. That's why squire over too. So that's a point one one. What's the point in next two one Next one we have fax. Fax. It's the Contra negative two times each with a power off ninety one. Why? Why, if they caught you negative two times each with a part ofthe next one. I have x Y you seek Or to Cyril. So half the court. You or Ham's Inter Negative, too. This is acquitted and zero things off. X X is less than zero This two points Uh, no con maximum as it's appoint one next to one, and there's a point next. One one off Ex LAX If they go to two times the next one. One wife. His record two times to ninety one on a fax. Why see what? Zero. So is a torture or Tom City to meet you, too It's great, isn't zero since half XX is Colton and zero. So there's two points a local minimal. That is a point zero zero. We have half XX. It's equal to after. Why? Why? It's equal to zero. Ex ally. It's the culture one. So is that going to make you one last time? Zero. So it is a saddle point. Now let's look at this. A graph for the function so we can see that is a point to one one next one next one. It is a local maximum and that is point ninety one one one two one. They are local minimum, but that is a point of zero Cyril. It is neither local, maximum nor local minimal, so it is a subtle point.