Fnd the absolute maximum and minimum of the function - fx

Question

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.

Answer 1

The whole data that have many questions on basis of your text book give answer of each question Question 1. Using the technique outlined in Section of the textbook, and illustrating the working, sketches the graph of each of the subsequent functions. Note: you don’t need to consider f''(x), concavity and points of inflection. (a) f(x) = (1/4)(x2 - 4)2 (b) f(x) = 8/x2v(x+5) Question 2. Discover the absolute maximum and minimum of the function f(x) = x2/3(x2 - 6) for x ? [-1, 3] Express your answers in easy exact form. Question 3. A company wants to manufacture an open cylindrical bucket of volume 10 litres (10000 cm3). The plastic utilized for the base of the bucket costs 0.05 cents per cm2 while the plastic employed for the curved side of the bucket costs 0.02 cents per cm2. Find the radius and height of the bucket for that the bucket has minimum cost. What is the minimum cost? Demonstrate all the reasoning and evaluate your answers to 2 decimal places.