Find the critical points for the function f(x, y) = 32xy — 0.25(x + y)² and classify each as a local maximum, local minimum, saddle point, or none of these. critical points: (give your points as a comma separated list of (x,y) coordinates.) classifications: (give your answers in a comma separated list, specifying maximum, minimum, saddle point, e for each, in the same order as you entered your critical points) or none

Consider an axisymmetric feeding bowl as shown on the left below. Its cross-section is shown on the right with the axis of symmetry aligned along the y-axis. The top curve of the cross-section is given by the function b. What is the capacity of this bowl? Capacity= cm³ c. Find the volume of water inside the bowl if the water level is 3.3 cm measured from the bottom. Volume of water = 1 961 y = C 961 The horizontal base joins the endpoints of the top curve. Both x and y are in cm. You may need to use a computer algebra system to solve some of the following problems. Round all your answers to at least 3 significant figures. a. Assume that the bowl is solid and is made with plastic. Find the amount of plastic (as a volume) required to make this bowl. Amount of plastic = cm³ cm3 -x4 (9-x) 1 4 -x¹ (9 + x) y 0≤x≤9.1 -9.1 < x < 0 X

Please answer the question in its entirety.

find domain, range and graph a function