(a) Find a number x in the closed interval. such that the sum of the number...

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(a) Find a number x in the closed interval. such that the sum of the number and its reciprocal is as small as possible. Enter the exact answer. (b) Find a number x in the closed interval such that the sum of the number and its reciprocal is as large as possible. Enter the exact answer. X= A cone-shaped paper drinking cup is to hold 80 cm of water. Find the height and radius of the cup that will require the least amount of paper. NOTE: Enter the exact answers. Radius= Height= cm cm A closed rectangular container with a square base is to have a volume of 2250 in. The material for the top and bottom of the container will cost $2 per in, and the material for the sides will cost $3 per in2. Find the dimensions of the container of least cost. Let x be the length of each edge of the base and y be the height. Enter the exact answers. X= y= inches inches (a) Find a number x in the closed interval. such that the sum of the number and its reciprocal is as small as possible. Enter the exact answer. (b) Find a number x in the closed interval such that the sum of the number and its reciprocal is as large as possible. Enter the exact answer. X= A cone-shaped paper drinking cup is to hold 80 cm of water. Find the height and radius of the cup that will require the least amount of paper. NOTE: Enter the exact answers. Radius= Height= cm cm A closed rectangular container with a square base is to have a volume of 2250 in. The material for the top and bottom of the container will cost $2 per in, and the material for the sides will cost $3 per in2. Find the dimensions of the container of least cost. Let x be the length of each edge of the base and y be the height. Enter the exact answers. X= y= inches inches