Derivatives and Optimization

Hosena, George

1. Differentiate y = csc x cot x

2. A piece of pipe is being carried down a hallway that is 10 feet wide. At the end of the hallway, there i a right-angled turn and the hallway narrows down to 8 feet. What is the longest pipe that can be carried (always keeping it horizontal) around the turn of the hallway.

Juridico, Aaron

1. Find the derivative of y = 4cos(6x^2 + 5)

2. A sheet of cardboard 3ft by 4ft will be made into a box by cutting equal sided squares from each corner and folding up the four edges. What will be the dimension of the box with the largest volume?

Lim, Paul

1. A rectangle of maximum possible are to fit in the region is bounded by the parabola y = 12 - x^2 and the y-axis. What is the largest rectangle that fits?

2. What is the derivative of g(t) = 5^t

Lozada, Rayshelle

1. A florida citrus grower estimates that if 60 orange tress are planted; the average yield per tree will be 400 oranges. The average yield will decrease by 4 oranges per tree for each additional tree planted on the same acreage. How many trees should the grower plant to maximize the total yield?

2. Differentiate f(x) ln(x) log (x) base 2 at x = 2

Magnayon, Francis

1. Differentiate y = sin^2 4x + cos^2 4x

2. Find the largest area of the rectangle of largest area that has its base on the x-axis and its to other vertices above the x-axis and lying on the parabola y=8-x^2

Mena, James

1. You are trying to build a cylindrical can. You want the can to be able to hold 60 cubic inches of material. What dimensions will minimize the cost of the can?

2. Differentiate f(t) = e^t / sin t

Olano, Jerome

1. A farmer needs 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?

2. Differentiate g(x) = 3 sec (x) - 10 cot (x)

Pelayo, Jake

1. A window is being built and the bottom is a rectangle and the top is semicircle. If there's 12m of framing materials, What must be the dimensions of the window be to let in the most light?

2. Differentiate g(x) = (x csc x) / (3 - csc x)

Rabi, Gabriel

1.Differntiate y = 5 sin x - 6 cos x

2. Differentiate y = 4 sin x - 7 cos x

Roldan, John Gil

1. Differentiate y = 3 sin x - 4 cos x

2. Determine the area of the large rectangle that can be inscribed in a circle of radius 4.

Sungcados, Elle

1. Differentiate y = 3 sin x - 4 cos x

2. We want to build a box whose length of the base is 6 times the base width and the box will enclose

20 in^3. The cost of the material of the sides is Php 3.00 per in^2 and the cost of the top and the bottom is Php 15.00 per in^2. Determine the dimensions of the box that will maximize the cost.

Suralta, Brent

1. Differentiate f = cos^3 10x sin^2 3x + tan 5x

2. A cylinder is inscribed in a cone with a height of 10cm and a base radius of 5cm. Find the approximate values of r and h for which the volume of the cylinder is a maximum.

Taberna, Catherine

1. We are going to fence in a rectangular field. If we look at the field from above the cost of the vertical sides are $10/ft, the cost of the bottom is $2/ft and the cost of the top is $7/ft. If we have $700 determine the dimensions of the field that will maximize the enclosed area. (Source: http://tutorial.math.lamar.edu/Problems/CalcI/Optimization.aspx)

2. The position of an object is given by s(t) = 2 + 7 cos (t). Determine all the points where the object is not moving. (Source:http://tutorial.math.lamar.edu/Problems/CalcI/DiffTrigFcns.aspx)