Unit 4: Extensions Instructions There are 10 questions in this Assessment Opportunity. For full marks, show all work for each question. 1. Find the derivative. a. y = sin x b. y = sin x c. y = cos(4x + 9) d. y = cos (x + 3) e. y = x sin(x + 5) f. y = 5et g. y = e 5x h. y = xe 3x+1 i. y = In(x + 3) J. y = 5In (x + 4) k. y = 5* 1. y = (x + 2) (x + 2x+ 1)3 m. y = In(sin x) n. y = (x+ Inx)Find the equation of the tangent line to the function y = in (x2 2) when x = 3. 2 Find the equation of the tangent line to the curve 3: = cos xwhen x = %. Your solution should use radian measure. Find the intervals of increasing/decreasing for the function f (x) = x3ex Find the minimum value(s) of the function f(x) = eJr 2x. . The position of a particle as it moves horizontally is described by the given equation 5' = stnt cost, 0 S t g 211:. Ifs is the displacement in metres and tis the time in seconds, nd the maximum and minimum displacements. For questions #7 to, solve the problem by following the procedure for solving an optimization problem. Show all your steps. include a concluding statement that summarizes your answer and includes the correct units. 7. 10. An apple orchard now has 80 trees per hectare and the average yield is 400 apples per tree. For each additional tree planted per hectare the average yield per tree is reduced by approximately four apples. How many trees per hectare will give the largest crop of apples? . Time to Travel advertises a package plan for an Arizona vacation. The fare for the ight is $400lperson plus $8lperson for each unsold seat on the plane. The plane holds 120 passengers and the flight will be cancelled if there are fewer than 25 passengers. What number of passengers will maximize revenue? . An open-topped storage box with a square base has a capacity of 5 m3. The material for the sides cost $1 .60lm2, while the material for the bottom costs $2.00lm2. Find the dimensions that will minimize the cost of making the box. A rectangular piece of paper with perimeter 100 cm is to be rolled to form a cylindrical tube. Find the dimensions of the paper that will produce a tube with maximum volume