(a) Find an equation of the tangent line to the curve y = 2/(1 + e-*) at the point (0, 1). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. Determine f"(x). a. f(x) = cos x b. f(x) = cos x cot xI Determine the equation of the tangent to the curve dened by y = x - e that is parallel to the line represented by 31: - y 9 = 0. Lorianne is studying for two different exams. Because of the nature of the courses, the measure of stud}; effectiveness on a scale from 0 to 10 for the rst course is E1 = 0.6(9 + re '3), while the measure for the second course I' is E; = 0.5(10 + of\"). Lorianne is prepared to spend up to 30 h, in total, studying for the exams. The total effectiveness is given by f\") = E1 + E2. How should this time be allocated to maximize total effectiveness