1. Clearly state what each of your variables denotes. (a) A lamp-maker manufactu

Question

1. Clearly state what each of your variables denotes.

(a) A lamp-maker manufactures her lamps at $4 each and sells them at $6 each and, at this sales price, sells 3,000 lamps per month. The manufacturer wishes to increase her revenue and is considering increasing her sales price, however, her market research suggests that for each 50 cent increase she will sell 350 fewer lamps each month. Assuming a linear relationship between the sales price and the number of lamps sold, express the manufacturer’s monthly profit as a function of the increase in her sales price.

(b) A rectangular box on a square base is to have a surface area of 150 square centimeters. Express the volume of the box as a function of the length of its base.

(c) I built a storage shed in the shape of a box on a square base. The material that I used for the base cost $4 per square foot, the material for the roof cost $2 per square foot, and the material for the sides cost $2.50 per square foot, and I spent $450 altogether on material. Express the volume of the shed as a function of the length of its base.

2. Sketch the graph of any function y = f(x) with the following characteristics. Draw large, neat diagrams that clearly display all the given information.

(a)

• Hole at x=2

• Horizontal asymptote at y = 2

• Vertical asymptotes at x = 2 and x = 4

• x-interceptsatx=6, x=4 and x=6

• y-intercept at y = 2

(b)

• f(6)=4

• Holes at x=0 and x=5

• Horizontal asymptote at y = 2

• Vertical asymptotes at x = 2 and x = 4

• x-interceptsatx=4,x=1,x=1 and x=2

• y-intercept at y = 1

3.The function y= (2x+3)/(4x + 5)^2 has as its derivative y=8x+14 /(4x + 5)^3

Find an equation for the tangent to the graph of y at x = 1.

Explanation / Answer

3 equation of tangent is given by y-y1 = m(x-x1),

Where m = y' and x = -1 should be substituted to get m slope value = 16;

X1 = -1 given and we get y1 by substituting x1 in y = 1;

The equation is y-1= 16(x+1) ;

16x -y +17 = 0 is the required equation

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