1. [-/2 Points] DETAILS MY NOTES Consider the following. ((x, y) = 2x2 + y2 - 4x - 6y + 11 Find the point (x, y) where ((x, y) has a possible relative maximum or minimum. (Give the exact point.) (x, v) = C Submit Answer 2. [-/4 Points] DETAILS MY NOTES Consider the following. f(x, y) = 2x2 - 2y3 - 16x + 24y + 32 Find the points (x, y) where f(x, y) has a possible relative maximum or minimum. (Give the exact points.) (x, v) = (point with smaller y-value) ( x , y ) = (point with larger y-value) Submit Answer SKIP TO CO IGATION 3. [-/15 Points] DETAILS MY NOTES Attention! You have only TWO submissions for each of the multiple choice answers. Use your submissions wisely. Consider the following. f(x, y) = 6xy2 - 2x3 - 34 Find all the first and second partial derivatives and D(x, y). of ox Z 04 = azf D(x, y) - Both first partial derivatives of the function f(x, >) are zero at the points below. Use the se erivative test is inconclusive, so state. (a) (0, 0) O relative max O relative min O neither max nor min O inconclusive (b) (1, 1) O relative max O relative min O neither max nor min O inconclusive (c) (1, -1) O relative max O relative min O neither max nor min O Inconclusive Submit Answer 1. [-/3 Points] DETAILS MY NOTES Attention! You have only TWO submissions for the multiple choice answer. Use your submissions wisely. Consider the following. f(x, y) = x2 - 2xy + 32 + 4x-24y +34 test is inconclusive, so state. 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 ( x , y ) = Select- Submit Answer 5. [-/9 Points] DETAILS MY NOTES Attention! You have only TWO submissions for each of the multiple choice answers. Use your submissions wisely. Consider the following. R(x, y) = x2 + 4xy + 24 Find the exact points (x, y) where f(x, y) has a possi second-derivative test is Inconclusive, so state. num or minimum. Then use the second-derivative test to determine, If possible, the nature of f(x, y) at each of these points. If the (x, y) - ...Select- v (smallest x-value) ( x , v ) = -Select- (x , y ) = -Select- (largest x-value) Submit Answer 6. [-/6 Points] DETAILS MY NOTES U.S. postal rules require that the length plus the girth of a package cannot exceed 84 inches in order to be mailed. Find the ex greatest volume that can be mailed. [Note: From the figure below we see that 84 - (length) + (girth) - / + (2x + 2y).] inches inches inches Submit Answer 7. [-/6 Points] DETAILS MY NOTES A monopolist manufactures and sells two competing products, call them I and II, that cost $46 and $34 per unit, respectively, to produce. The revenue from marketing x units of product I and y units of product II Is R(x, y) = 114x + 126y - 0.04xy - 0.1x2 - 0.2y2. Find the exact values of x and y that maximize the monopolist's profits. Submit Answer 8. [-/4 Points] DETAILS MY NOTES Given the line y - 2.5x + 5, find the sum of the squared errors (also known as the error sum of squares or the error), E, for the three points (1, 4), (2, 5) and (4, 7). (Give an exact answer. Exact answer means give your answer as a fraction or a terminating decimal, DO NOT round.) E = Submit Answer 9. [-/12 Points] DETAILS MY NOTES In this question, you will find the least-squares line, y = Ax + B through the points (0, -1), (1, 4), (3, 5) and (4, 11). 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.) We want to find the values of A and B that both derivatives equal to zero. calculate the partial derivatives. (Give answers in terms of A and B.) Set both partial derivatives equal to zero. Rearrange the equation of = 0 to give A In terms of B. Now, substitute the above into the equation ag = 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.) 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.) Submit Answer 10. [-/4 Points] DETAILS MY NOTES Consider the following data points. (1, 10) ( 2 , 5 ) ( 5, 3) Use partial derivatives to obtain the formula for the best least-squares fit to the data points. v(x) =