Page Design

[nycmathguy]

Section 2.6
Question 72

Can you do parts (a) and (c)? I will do (b).

 

[MathLover1]

(a)

Total area of the page:
area=xy

contains 30in^2 print (also rectangle)=> the lengt=x-4, the height=y-2

(x-4)(y-2)=30 ........solve for y
y-2=30/(x-4)
y=30/(x-4)+2

then

area=x*(30/(x-4)+2 )
area=(2x(x + 11))/(x - 4)


(c)
least amount of paper

find out where derivative is equal to zero

(d/dx)(2x(x + 11))/(x - 4)

will be equal to zero only if (x^2-8x-44)=0

=>x = 4 - 2 sqrt(15) or x = 2 (2 + sqrt(15))

for minimum use x = 2 (2 + sqrt(15))

Minimum

(2(2+sqrt(15)), (120+38sqrt(15))/sqrt(15) )

 

[nycmathguy]

(a)

Total area of the page:
area=xy

contains 30in^2 print (also rectangle)=> the lengt=x-4, the height=y-2

(x-4)(y-2)=30 ........solve for y
y-2=30/(x-4)
y=30/(x-4)+2

then

area=x*(30/(x-4)+2 )
area=(2x(x + 11))/(x - 4)


(c)
least amount of paper

find out where derivative is equal to zero

(d/dx)(2x(x + 11))/(x - 4)

will be equal to zero only if (x^2-8x-44)=0

=>x = 4 - 2 sqrt(15) or x = 2 (2 + sqrt(15))

for minimum use x = 2 (2 + sqrt(15))

Minimum

(2(2+sqrt(15)), (120+38sqrt(15))/sqrt(15) )

1. I will do part (b).
2. Can you do part (c) without calculus?

 

[MathLover1]

part (c) doesn't work without calculus, you have to find f'(x)

 

[nycmathguy]

part (c) doesn't work without calculus, you have to find f'(x)

Ron Larson does not say anything about finding limits of functions involving positive or negative infinity.

 

[nycmathguy]

(a)

Total area of the page:
area=xy

contains 30in^2 print (also rectangle)=> the lengt=x-4, the height=y-2

(x-4)(y-2)=30 ........solve for y
y-2=30/(x-4)
y=30/(x-4)+2

then

area=x*(30/(x-4)+2 )
area=(2x(x + 11))/(x - 4)


(c)
least amount of paper

find out where derivative is equal to zero

(d/dx)(2x(x + 11))/(x - 4)

will be equal to zero only if (x^2-8x-44)=0

=>x = 4 - 2 sqrt(15) or x = 2 (2 + sqrt(15))

for minimum use x = 2 (2 + sqrt(15))

Minimum

(2(2+sqrt(15)), (120+38sqrt(15))/sqrt(15) )

The area function found in part (a) is
(2x(x + 11))/(x - 4).

Setting the denominator to 0 and solving for x, I get 4. The domain for the area function is all real numbers except for x = 4.

You say?

 

[MathLover1]

correct

 

[nycmathguy]

correct

You did all the hard work. Part (b) is super easy. I give you the credit. By the way, I have a real hard time creating functions or equations from written information. For example, part (a) here is not so easy for me.

 

[MathLover1]

most important thing is read carefully what is given and what you need to find

 

[nycmathguy]

most important thing is read carefully what is given and what you need to find

I always read math applications several times. Let's face it. Some questions easier to grasp than others. By the way, we are done with Section 2.6. Moving on to Section 2.7 or Nonlinear Inequalities.