Reference no: EM13905372

Question 1. Using the method outlined in Section 5.4 of the textbook, and showing the working, sketch the graph of each of the following functions. Note: you do not need to consider f′′(x), concavity and points of inflection.

(a) f(x) = (1/4)(x² - 4)²

(b) f(x) = 8/x²√(x+5)

Question 2. Find the absolute maximum and minimum of the function

f(x) = x^2/3(x² - 6) for x ∈ [-1, 3]

Express your answers in simple exact form.

Question 3. A company wants to manufacture an open cylindrical bucket of volume 10 litres (10000 cm³). The plastic used for the base of the bucket costs 0.05 cents per cm² while the plastic used for the curved side of the bucket costs 0.02 cents per cm². 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.

Question 4. (a) Find dy/dx for xy³ + √(x² + 5y) = 5

(b) Show that the point (x, y) = (2, 1) lies on the curve defined by the equation in part (a), and find the slope of the tangent line at this point.