Question 4 [5 marks] Function f consists of the bottom half of the circle with center the origin and radius 2 and the line segment from the point (2,0) to the point (4,5). Explain all your steps when you do the following: (4.1) Find an expression for the function f. (4.2) Find the total area between the graph of the function f and the x-axis. (4.3) Give the value of ??? f(x)dx. Question 5 [6 marks] Consider function f(x) = x3(x - 4). Motivate all your answers. (5.1) Use the Closed Interval Method to find the absolute extreme values of f on [-2, 2]. (5.2) Determine if f has any local extreme values or inflection points on [-2, 2]. Question 6 [4 marks] A wooden container with a square base and an open top must have a volume of 32 000 cm3. Determine the dimensions of the box that minimize the amount of paint needed to paint the outside areas of the container.
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To find the function's domain, we need to figure out what x-values the function takes. So, we start by finding the interval [-2,2] and then extending it downwards by 2 units. This gives us [-4,0]. Show more…
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