Activity # 2. Find the solution of each of the following optimization problems 1. A particle moves along a coordinate axis. Its position at time tis given by 50) = sin(2t) + cos(3 1'). What is the velocity of the paiticle at time t : E ? 2. A particle moves along a coordinate axis. Its position at time tis given by s(t) = sin (4:). Find its acceleration at time t. (Hint: acceleration is the second derivative of the function). 3. The total cost of x boxes of JST cookies C pesos, where C(x) = 0.0048x3-O.96x2+144x+14400. In t weeks production is estimated to be x = 1600 + 100t boxes. a. Find the marginal cost C'(x) b. Find the rate with respect to time t that the cost is changing. (Hint: Apply the Change Rule: C'(t) ). c. Use b, to determine how fast costs are increasing when t = 2weeks. Include units in the nal answer. Activity #3 Find the derivative of the following using implicit differentiation. 1. x2 + y3 = 4 2. ex siny = x x 3. ? = I IV. Log Me In Discuss the implicit form of 2x3 =(3xy+1)2