Question 1

A rectangular beam will be cut from a cylindrical log of radius  inches.Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth.Find the dimensions of the strongest beam that can be cut from the cylindrical log. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

887.0

Question 2

Find the slant asymptote of the graph of  using the curve-sketching guidelines.
A) 
B) 
C) 
D)

Accepted Answer

883.0

Question 3

Find the dimensions of the rectangle enclosed in the semicircle  with the largest possible area. 
A) 
B)5 in.  7 in.
C) 
D)

Accepted Answer

888.0

Question 4

Let P (x) and Q (x) be polynomials.Find  if the degree of P (x) is 2 and the degree of Q (x) is 6.
A)9
B)5
C) 
D)0
E)4

Accepted Answer

875.0

Question 5

Find two positive numbers whose product is  and whose sum is a minimum.
A)6, 24
B)2, 72
C) 
D)3, 48
E)

Accepted Answer

886.0

Question 6

Identify any transitional values of  at which the basic shape of the curve changes. 
A) 
B) 
C) 
D)

Accepted Answer

885.0

Question 7

Find  
A) 
B) 
C) 
D) 
E)None of these

Accepted Answer

891.0

Question 8

A manufacturer has been selling 1,200 television sets a week at $400 each.A market survey indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60 per week.Find the demand function.
A) 
B) 
C) 
D) 
E)

Accepted Answer

889.0

Question 9

The graph of the derivative  of a continuous function f is shown.On what intervals is  decreasing?  .
A) 
B) 
C) 
D) 
E)None of these

Accepted Answer

873.0

Question 10

What can you say about point of inflation for  ?
A)point of inflation goes away from the origin
B)point of inflation goes away from 
C)point of inflation gets closer to the origin
D)point of inflation gets closer to

Accepted Answer

884.0

Question 11

Find the limit. 
A) 
B) 
C) 
D)

Accepted Answer

876.0

Question 12

A skydiver leaps from a helicopter hovering high above the ground.Her velocity  sec later and before deploying her parachute is given by  where  is measured in meters per second.What is her terminal velocity? Hint: Evaluate 
A)54 m/sec
B)8.1 m/sec
C)87 m/sec
D)62.1 m/sec

Accepted Answer

877.0

Question 13

Find the intervals where  is increasing and where it is decreasing.
A)increasing:  decreasing: 
B)   increasing: decreasing:
C)increasing:  decreasing: 
D)   increasing: decreasing:

Accepted Answer

874.0

Question 14

The size of the monthly repayment  that amortizes a loan of  dollars in  years at an interest rate of  per year, compounded monthly, on the unpaid balance is given by  The value of  can be found by performing the iteration  A family secured a loan of $360,000 from a bank to finance the purchase of a house.They have agreed to repay the loan in equal monthly installments of $2342 over 25 years.Find the interest rate on this loan.Round the rate to one decimal place.
A)4.1%
B)5.1%
C)6.1%
D)7.1%

Accepted Answer

890.0

Question 15

Evaluate the limit using  Rule.
A)6
B) 
C)12
D)27

Accepted Answer

879.0

Question 16

Find the critical number(s), if any, of the function 
A)3
B) 
C) 
D)

Accepted Answer

872.0

Question 17

Evaluate the limit. 
A)-5
B) 
C) 
D)1
E)0

Accepted Answer

881.0

Question 18

Evaluate the limit. 
A)9
B)0 
C) 
D)

Accepted Answer

878.0

Question 19

Evaluate the limit. 
A)2
B) 
C)0
D) 
E)

Accepted Answer

880.0

Question 20

Find the limit. 
A) 
B) 
C) 
D)5
E)0

Accepted Answer

882.0

Quiz 4: Applications of Differentiation

A rectangular beam will be cut from a cylindrical log of radius inches.Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth.Find the dimensions of the strongest beam that can be cut from the cylindrical log.

Find the slant asymptote of the graph of using the curve-sketching guidelines.

Find the dimensions of the rectangle enclosed in the semicircle with the largest possible area.

Let P (x) and Q (x) be polynomials.Find if the degree of P (x) is 2 and the degree of Q (x) is 6.

Find two positive numbers whose product is and whose sum is a minimum.

Identify any transitional values of at which the basic shape of the curve changes.

Find

A manufacturer has been selling 1,200 television sets a week at $400 each.A market survey indicates that for each $30 rebate offered to the buyer, the number of sets sold will increase by 60 per week.Find the demand function.

The graph of the derivative of a continuous function f is shown.On what intervals is decreasing? .

What can you say about point of inflation for ?

Find the limit.

A skydiver leaps from a helicopter hovering high above the ground.Her velocity sec later and before deploying her parachute is given by where is measured in meters per second.What is her terminal velocity? Hint: Evaluate

Find the intervals where is increasing and where it is decreasing.

Evaluate the limit using Rule.

Find the critical number(s) , if any, of the function

Evaluate the limit.

Evaluate the limit.

Evaluate the limit.

Find the limit.