SOLUTION: Given that (x + y) ^ 2 - 3x + 2y = 0 , find; i) dy/dx ii) the value of (d²y)/(dx²) at point (0,0)

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Question 1204162: Given that (x + y) ^ 2 - 3x + 2y = 0 , find;
i) dy/dx
ii) the value of (d²y)/(dx²) at point (0,0)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
%28x+%2B+y%29+%5E+2+-+3x+%2B+2y+=+0

2%28x%2By%29%281%2Bdy%2Fdx%29-3%2B2expr%28dy%2Fdx%29=0

2%28x%2By%29+%2B+2%28x%2By%29expr%28dy%2Fdx%29-3%2B2expr%28dy%2Fdx%29=0 

2%28x%2By%29expr%28dy%2Fdx%29%2B2expr%28dy%2Fdx%29=+3-2%28x%2By%29

expr%28dy%2Fdx%29%282%28x%2By%29%2B2%29=+3-2%28x%2By%29

dy%2Fdx=%283-2%28x%2By%29%29%2F%282%28x%2By%29%2B2%29

dy%2Fdx=%283-2x-2y%29%2F%282x%2B2y%2B2%29



Since this equation contains dy%2Fdx we need to find what dy%2Fdx is when (x,y) = (0,0)

matrix%281%2C3%2Cexpr%28dy%2Fdx%29%2Cwhen%2C%22%28x%2Cy%29=%280%2C0%29%22%29%22%22=%22%22%283-2%2A0-2%2A0%29%2F%282%2A0%2B2%2A0%2B2%29%22%22=%22%223%2F2

matrix%281%2C3%2Cexpr%28d%5E2y%2Fdx%5E2%29%2Cwhen%2C%22%28x%2Cy%29=%280%2C0%29%22%29%22%22=%22%22%22%22=%22%22
%28%282%29%28-2-3%29-%283%29%282%2B3%29%29%2F2%5E2%22%22=%22%22%28%282%29%28-5%29-%283%29%285%29%29%2F4%22%22=%22%22-25%2F4

Edwin