6. Consider the curve given by the equation 23,3 + y2 i y5 : x4 7 2m3 + m2. Find all points at which the tangent line to the curve is horizontal or vertical. Be sure to use a graphing utility to plot this implicit curve and to visually check the results of algebraic reasoning that you use to determine where the tangent lines are horizontal and vertical. 8. Implicit differentiation enables us a different perspective from which to see why the rule dm Jew] : a? 111(a) holds, if we assume that Eli[IMM] : 3}. This exercise leads you through the key steps to do so. a. b. Let y : am. Rewrite this equation using the natural logarithm function to write x in terms ofy (and the constant a). Differentiate both sides of the equation you found in (a) with respect to x, keeping in mind that y is implicitly a function of x. Solve the equation you found in (b) for 3: and then use the definition ofy to write 3: solely in terms of x. What have you found