(1 point) Please answer the following questions about the function f(x)=(x + 10)(4-2). Instructions: If you...

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(1 point) Please answer the following questions about the function f(x)=(x + 10)(4-2). Instructions: If you are asked to find - or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if you are asked to find an interval or union of intervals, and enter { } if the interval is empty. (a) Find the critical numbers of f, where it is increasing and decreasing, and its local extrema. Critical numbers x = Increasing on the interval Decreasing on the interval Local maxima x = Local minima x = (b) Find where f is concave up, concave down, and has inflection points. Concave up on the interval Concave down on the interval Inflection points x = (c) Find any horizontal and vertical asymptotes of f. Horizontal asymptotes y = Vertical asymptotes x = (d) The function f is ? because ? for all x in the domain of f, and therefore its graph is symmetric about the ? (e) Sketch a graph of the function f without having a graphing calculator do it for you. Plot the y-intercept and the x-intercepts, if they are known. Draw dashed lines for horizontal and vertical asymptotes. Plot the points where f has local maxima, local minima, and inflection points. Use what you know from parts (a) and (b) to sketch the remaining parts of the graph of f. Use any symmetry from part (d) to your advantage. Sketching graphs is an important skill that takes practice, and you may be asked to do it on quizzes or exams. (1 point) A cylinder is inscribed in a right circular cone of height 3.5 and radius (at the base) equal to 2.5. What are the dimensions of such a cylinder which has maximum volume? Radius = Height = (1 point) If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = (include units) (1 point) A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use? Length of fence = feet. (1 point) Please answer the following questions about the function f(x)=(x + 10)(4-2). Instructions: If you are asked to find - or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if you are asked to find an interval or union of intervals, and enter { } if the interval is empty. (a) Find the critical numbers of f, where it is increasing and decreasing, and its local extrema. Critical numbers x = Increasing on the interval Decreasing on the interval Local maxima x = Local minima x = (b) Find where f is concave up, concave down, and has inflection points. Concave up on the interval Concave down on the interval Inflection points x = (c) Find any horizontal and vertical asymptotes of f. Horizontal asymptotes y = Vertical asymptotes x = (d) The function f is ? because ? for all x in the domain of f, and therefore its graph is symmetric about the ? (e) Sketch a graph of the function f without having a graphing calculator do it for you. Plot the y-intercept and the x-intercepts, if they are known. Draw dashed lines for horizontal and vertical asymptotes. Plot the points where f has local maxima, local minima, and inflection points. Use what you know from parts (a) and (b) to sketch the remaining parts of the graph of f. Use any symmetry from part (d) to your advantage. Sketching graphs is an important skill that takes practice, and you may be asked to do it on quizzes or exams. (1 point) A cylinder is inscribed in a right circular cone of height 3.5 and radius (at the base) equal to 2.5. What are the dimensions of such a cylinder which has maximum volume? Radius = Height = (1 point) If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Volume = (include units) (1 point) A rancher wants to fence in an area of 1000000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use? Length of fence = feet.