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1.A rectangle has one vertex on the line y=L-Fx,x>0 , another at the origin, one on the positive x-axis, and one on the positive y-axis. Find the largest area A that can be enclosed by the rectangle. Show all your work and include a sketch with labels of all important features. (Hint: Start by drawing a diagram, label the base of the rectangle as x, and write the area, A, as a function of x. â€¦)

Where F = 5, L =4

SOL : A = f(x)= x * (-5x+4) ; the x is the base while y(x)=-5x+4 is the

height.

and the domain of x is 0<x<(4/5)

To get critical point x= 4/10 which is

where the maximum occurs at y= .8 ( took the derivative )

2.A drum in the shape of a right circular cylinder is required to have a volume of cubic centimeters. The top and bottom are made of material that costs FÂ¢ per square centimeter; the sides are made of material that costs LÂ¢ per square centimeters. (Hint: The formula for the volume of a right circular cylinder is V=pie r^2 , where r is the radius of the circular base and h is the height of the cylinder. The surface area of the sides can be determined by cutting the cylindrical shell vertically and flattening it out to get a rectangle whose dimensions can be determined.)

a)Express the total cost C of the material as a function of the radius r of the cylinder.

b)What is the cost if the radius is 25 cm?

c)Graph C=C(r) . Using the graph, for what value of r, approximately, is the cost C least?

Where F = 5, L =4

SOl : C= L(2*pi*r*h)+F(2*pi*r^2);

C(r) = L(2*pi*r*(2*pi*r/sqrt(3))+F(2*pi*r^2); Here height is

expressed in terms of r . The ratio used to find h in terms of r is

30-60-90 degree triangle; (2*pi*r)/(h) = sqrt(3)/1

3.Design a polynomial function with the following characteristics: degree 6; exactly four real zeros, one of multiplicity 3 at x= -F ; y-intercept at F, behaves like y = -Lx^6 for large values of |x| . Give the formula and a complete graph

Where F = 5, L =4

???

4.Create a rational function that has the following characteristics: crosses the x-axis at F; touches the x-axis at -L ; has one vertical asymptote at x=-L-1 and another at x=F+1 ; and has one horizontal asymptote, y=F . Give the formula and a complete graph

Where F = 5, L =4

SOL: Crosses X-Axis @ g

touches X-Axis @ -4

Vertical asymtote X= -4-1 = -5

Veetical asymtote x= 5+1 = 6

Horizontal asymtote y=5

5X 1

--- X ----

(X+5) (X-6)

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# Homework Help: Please Help Pre-Cal

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