What is this multiplying and dividing strategy? The only way I\'ve learned to fi

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What is this multiplying and dividing strategy? The only way I've learned to find critical points was taking the partial derivative of x and setting it to zero, and then setting the partial derivative of y and setting it to zero. Can someone please provide further explanation?

4. Find all critical points of the functionfx,y)9x+443 elect from A-(2,3) B-(-2,3) C-(2-3) D-(-2-3) Note 432 = 2133 a. A,B,C,D b. E,F,G,H c. A,D Correct d. B,C e. E,H Solution 9x2 +4y2 + Multiply: xty-24-54-2431 xy-£6 Divide Multiply results. xy =x-£6. Divide results: xv -- Looking at x3y - 24, x and y must be both positive or both negative. So (2,3), (-2,-3) 54 9 ·=±4 3 Must have x2-4 x--2 -= ±6 . -+9 Must have y2-9

Explanation / Answer

this is nothing just a one way of calculating the points this is only

method of finding the x and y (critical points) but as you can see in this

also you really need a help of partial derivative so conclusion is that

partial derivative is important for finding critical points

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