6. NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work, even though the...

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6. NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Consider the function y = f(x) whose curve is given by the equation 2y2-6 = y sin x for y > 0. (a) Show that dy = y cos x 4y-sin x* (b) Write an equation for the line tangent to the curve at the point (0, 3). (c) For 0x and y > 0, find the coordinates of the point where the line tangent to the curve is horizontal. (d) Determine whether f has a relative minimum, a relative maximum, or neither at the point found in part (c). Justify your answer, 6. NO CALCULATOR IS ALLOWED FOR THIS QUESTION. Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number. Consider the function y = f(x) whose curve is given by the equation 2y2-6 = y sin x for y > 0. (a) Show that dy = y cos x 4y-sin x* (b) Write an equation for the line tangent to the curve at the point (0, 3). (c) For 0x and y > 0, find the coordinates of the point where the line tangent to the curve is horizontal. (d) Determine whether f has a relative minimum, a relative maximum, or neither at the point found in part (c). Justify your answer,