Math 251, Worksheet 5: 3.5, Implicit Differentiation 1. Let x2 + y2 = 16 (a) Using a graphing tool ( I suggest Desmos so you all can see the graph), sketch the graph. Draw a sketch in your work. (b) Using implicit differentiation, determine da dy (c) Where does the graph have horizontal tangent lines. Justify your reasoning and determine the equations of the lines. (d) Where does the graph have vertical tangent lines. Justify your reasoning and determine the equations of the lines. (e) Using your graphing tool, graph the curve with the tangent lines you found to verify your results, and give criteria for having horizontal and tangent lines to a curve. 2. Consider the curve x3 + y3 - 3xy = 0. (a) Using the graphing tool, sketch a graph of the curve. What feature of the graph is interest- ing? Using implicit differentiation, find a dy (b) Using the criteria you developed from 1(c), does the graph have a horizontal tangent line at (0, 0)? (c) Using the criteria you developed from 1(d), does the graph have a vertical tangent line at (0, 0)? (d) Are you surprised by your results from 2(b) and 2(c)? Explain your answer. Think about the "interesting" feature of the graph