Math 1271, Summer 2010, Worksheet 23.11. A farmer has 960 ft of fencing and wants to enclose a rectangular area and then divideit into 3 pens with fencing parallel to one side of the rectangle. What is the largest possibletotal area of the 3 pens?2. Find the dimensions of the rectangle of the largest area that has its base on the x axisand the other two corners above the x axis and lying on the parabola y = 75 − x2. For whatvalues of x is this rectangle defined?1Math 1271, Summer 2010, Worksheet 23.21. Sketch the graph of a function f (x) which is continuous and satisfies all of the followingconditions:(a) f0(x) > 0 when x < 0 or 3 < x < 6. Also, f0(x) < 0 when 0 < x < 3 or x > 6.(b) f00(x) > 0 when x < −2 or x > 6. Also, f00(x) < 0 when −2 < x < 3 or 3 < x < 6.2. Sketch the graph of a function f (x) which is continuous and satisfies all of the followingconditions:(a) f0(−3) = DNE, f0(0) = 0, f0(4) = DNE, f00(0) = 0.(b) f0(x) > 0 when x < −3 or x > 4. Also, f0(x) < 0 when −3 < x < 0 or 0 < x < 4.(c) f00(x) > 0 when x < −3, −3 < x < 0, or x > 4. Also, f00(x) < 0 when 0 < x <
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