Consider the following. f(x, y) = 3x + 5xy + 6y Find the exact point (x,...

   

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Consider the following. f(x, y) = 3x + 5xy + 6y Find the exact point (x, y) where f(x, y) has a possible relative maximum or minimum. Then use the second-derivative test to determine, if possible, the nature of f(x, y) at this point. If the second-derivative test is inconclusive, so state. (x, y) = ( Consider the following. f(x, y) = x - 2xy + 3y2 + 4x - 36y + 98 Find the exact point (x, y) where f(x, y) has a possible relative maximum or minimum. Then use the second-derivative test to determine, if possible, the nature of f(x, y) at this point. If the second-derivative test is inconclusive, so state. (x, y) = Consider the following data points. (1,8) (2,4) (4,3) Use partial derivatives to obtain the formula for the best least-squares fit to the data points. y(x) = In this question, you will find the least-squares line, y= Ax + B through the points (0, -3), (1, 2), (2, 6) and (4, 9). The error (sum of squared errors) is a function of A and B. State this function. (Give an answer in terms of A and B.) E = (A+B-2)2 + (24+B-6)2 + (44+B-9)2+(B+3) We want to find the values of A and B that minimize this function. As usual, we do this by calculating partial derivatives and then solving the simultaneous equations that result from setting both derivatives equal to zero. Calculate the partial derivatives. (Give answers in terms of A and B.) JE 2(A+B-2) + 4(24+B-6) +8(44+ B-9) a JE = 2(A+B-2) +2(24+B-6) +2(4A+B-9) + 2 (B+3) Set both partial derivatives equal to zero. Rearrange the equation = 0 to give A in terms of B. JE A A = Now, substitute the above into the equation = 0 and solve for B. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) B = Finally, find the value of A. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) A = Consider the following. f(x, y) = 3x + 5xy + 6y Find the exact point (x, y) where f(x, y) has a possible relative maximum or minimum. Then use the second-derivative test to determine, if possible, the nature of f(x, y) at this point. If the second-derivative test is inconclusive, so state. (x, y) = ( Consider the following. f(x, y) = x - 2xy + 3y2 + 4x - 36y + 98 Find the exact point (x, y) where f(x, y) has a possible relative maximum or minimum. Then use the second-derivative test to determine, if possible, the nature of f(x, y) at this point. If the second-derivative test is inconclusive, so state. (x, y) = Consider the following data points. (1,8) (2,4) (4,3) Use partial derivatives to obtain the formula for the best least-squares fit to the data points. y(x) = In this question, you will find the least-squares line, y= Ax + B through the points (0, -3), (1, 2), (2, 6) and (4, 9). The error (sum of squared errors) is a function of A and B. State this function. (Give an answer in terms of A and B.) E = (A+B-2)2 + (24+B-6)2 + (44+B-9)2+(B+3) We want to find the values of A and B that minimize this function. As usual, we do this by calculating partial derivatives and then solving the simultaneous equations that result from setting both derivatives equal to zero. Calculate the partial derivatives. (Give answers in terms of A and B.) JE 2(A+B-2) + 4(24+B-6) +8(44+ B-9) a JE = 2(A+B-2) +2(24+B-6) +2(4A+B-9) + 2 (B+3) Set both partial derivatives equal to zero. Rearrange the equation = 0 to give A in terms of B. JE A A = Now, substitute the above into the equation = 0 and solve for B. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) B = Finally, find the value of A. (Give an exact numerical answer with no variables. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) A =