Derivatives and Optimization : 2017

Agoy, Charlaine

1. Airplane tickets cost 200 pesos, if between 0 and 50 passengers are on the plane for each additional passenger over 50, the price per ticket will be reduced by 2 pesos for all passengers

2. Differentiate y = sin^3 (cos^3 x)

Almadovar, Anna

1. Differentiate g(x)=4π[cos(3πx) sin⁡(3πx)]

2. Find the dimensions that will minimize the cost of metal to make a cylindrical can that is able to store 0.25L of fluid

Asuncion, Mariah

1. Find the derivative of y = (-3x^2 - 5) / (cos2x^3)

2. An open box is to be made from a piece of metal 16 by 30 inches by cutting out squares of equal size from the corners and bending up the sides. What square should be cut out to create a box with the greatest volume. What is the maximum volume as well?

Asuncion, Tristan

1. A rectangle is inscribed in the region Quadrant I and II bounded by the x-axis and the parabola y = 9 - x^2 . Find the length and width of the rectangle of greatest parameter.

2. Differentiate f(x) = ln(sin(6x-1))

Baobao, Houston

1. Differentiate f(x) = cot x / 2x-3

2. A rectangular field is to be fenced off along the road. If 500 yards of fencing are available. What are the dimension of a field that produces the maximum area?

Berdin, Ivan

1. Find 2 positive numbers such that x + 2y = 50 and (x+1) (x+2) is a maximum.

2. We have a piece of cardboard that is 50 cm by 20 cm and we are going to cut out the corners and fold up the sides to form a box. Determine the height of the box that will give the maximum volume.

Bernabe, Mikaella

1. Differentiate y= z5—e2 ln (2

2. Find 2 positive numbers whose sum is 300 and whose product is a maximum.

Betoy, Karl

1. We need to enclose a rectangular field with a fence. We have 500 ft of fencing material and a building is on one side of the field and so we don't need nay fencing. Determine the dimension of the field that will enclose the largest area.

2. Differentiate f(x) = tan x

Buenabajo, Gabriel

1. A container in the shape of a right circular cylinder with no top has surface are of 3 ft^2. What height h and base radius r will maximize the volume of the cylinder?

2. Differentiate y = cot 5x^2

Cacanindin, Mark

1. Find the derivative of y = 3 sin^2 (5x^3)

Coloquio, Janmer

1. Four pens will be built side by side along a river by using 150 ft. of fencing. What dimensions will maximize the area of the pens ?

2. f(x) = cos x+1/x-1

Cruz, Rankin

1. Differentiate f(x) = cos x / (1+sin x)

2. We want to construct a box with a square base and we only have 10m^2 of material to use in the construction of the box considering that all the materials is used in the construction process. Determinte the maximum volume that the box can have.

Culilap, Manjelette

1. Airplane tickets cost $200 if between 0 and 50 passengers are on the plane. However each additional passenger over 50, the price per ticket is reduced by $2 for all passengers. For example if there are 52 passengers, then the cost per ticket for all passengers is $192. How many passengers will produce the maximum revenue?

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

Decena, Renn

1. A 15 ft ladder is resting against a wall. The bottom is initially 10 ft away and is being pushed towards the wall at 1/4 ft/sec. How fast is the top moving after 12 sec

2. Differentiate f(x) = cos (4x) cos^-1 (4x)

Deciembre, Christian

1. A disease has hit the city, the percentage of the population inflicted t days after the disease arrives is approximated by p(t) = 7t(e^(-t/12)) for the first 5 weeks. After how many days in the percentage of infected people at a maximum? What is the maximum percent of the population infected?

2. Differentiate f(x) = ln(sin(6x-1))

Del Rosario, Carlo

1. Differentiate y = 5^(sec x + tan x)

2. A rectangle is to be inscribed in a right triangle, the right triangle having the sides of 5cm, 12cm, and 13cm. Find the largest are of the rectangle.

Delos Santos, Vince

1. Find the derivative of y = (-2x^2 - 5) / (cos 2x^3)

2. A rectangular field is to be fenced off along a wall. If 200 yards of fencing are available, what are the dimensions of a field that produces the maximum area

Domingo, Kyron

1. Differentiate f(x) = (x^2 + 1) / (5x-3)

2. We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost $6/ft2. If the box must have a volume of 50ft3 determine the dimensions that will minimize the cost to build the box.