Sketch the graph of one continuous function f that has all of the following properties, calculus homework help

1. Sketch the graph of one continuous function f that has all of the following properties.
   • f(0) = 6 is an absolute maximum.
   • f(3) = 2 is an absolute minimum.
   • f has a critical point at x = 2 but no local maximum or local minimum value there.
2. A farmer has 850 meters of fencing material available to fence a rectan-
   gular field. He wants to fence the outside border of the field and then
   add two additional rows of fencing to divide the area into three regions
   of equal area (see diagram to the right). Find the dimensions of the
   original field that maximize its total area, and then find the maximum
   area.
3. A farmer wants to fence a rectangular area next to a straight river and then
   divide it in half to form two regions of equal area. He needs no fence along
   the river. The fence on the outer perimeter is a sturdy material costing
   per foot (solid lines in diagram), while the fence dividing the two pens in half
   costs only $1 per foot (dotted line in diagram). If the total area fenced is to
   be 120,000 square feet, find the minimum cost of the fencing material.
4. A total of $20 is available to construct a closed rectangular box with a square base. The
   material for the top and the bottom of the box costs $3 per square meter, while the
   material for the other four sides costs $2 per square meter. Find the dimensions of the
   box that maximize its volume.
5. The velocities of a sprinter at selected times over a 10-
   second race are given by the table to the right.
   1. (a) Give an underestimate and and overestimate for the total distance traveled by the sprinter during the
      race. Include units, and make it clear which answer is which.
   2. (b) Give your best estimate of the total distance traveled by the sprinter during the race.

This Table is for Question #5