the method mentioned in question 1 is showed after question 4 .

could you also show working out and answer as i would like to compare it to my work and fix any problemes i have thank you

5.4 Curve Sketching Graphics calculators have limitations and can be misleading if important points lie outside view. want to use calculus to determine behaviour of functions. Curve Sketching consider: 1. domain 2. yintercept, sitintercept (s) 3. vertical and horizontal asymptotes (if exist) 4. symmetry (if even or odd function) 5. critical points, relative extrema and where f is increasing and decreasing Use this information to sketch the graph. Possibly plot one or two more points to make the sketch 11101'6 accurate. 1. [23 marks] Using the method outlined in Section 5.4 of the textbook (also described in lectures). and showing the working, sketch the graph of each of the following functions. Note: you do not need to consider f "(1'). concavity and points of inflection (step [i]. (a) at] : 29:2(3: 1)(.1'- + 3) (b) fix] = 42;? 2. [7 marks] Find the absolute maximum and minimum of the function at) 2 (23:2 + nefa- for a: :5 [1,8] Express your answers in simple exact form. 3. [8 marks] A company wants to manufacture an open cylindrical bucket of volume 10 litres (10000 China}. The plastic used for the base of the bucket costs 0.08 cents per cm? while the plastic used for the curved side of the bucket costs 0.03 cents per cmz. Find the radius and height of the bucket for which the bucket has minimum cost. What is the minimum cost? Show all the reasoning and evaluate your answers to 2 decimal places. 4. [7 marks] (a) Find sly/dz for 23:23}? + 03:: + Ty = 22 (b) Show that the point (any) 2 (3. 1) lies on the curve dened by the equation in part (a), and nd the slope of the tangent line at this point