Question 1

Find the derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative of  .
A) 
B)...

Question 2

Find an equation of the line tangent to  at x = 3.
A) 
B) 
C) 
D)

Accepted Answer

To find the equation of the tangent line, we need to take the derivative of the function and evaluate it at x = 3. Using the power rule, we get:

f'(x) = 2x - 6

Evaluated at x = 3, we have:

f'(3) = 6 - 6 = 0

This means that the slope of the tangent line is 0. To find the y-intercept of the tangent line, we need to find the y-coordinate of the point on the original function where x = 3. Plugging x = 3 into the function, we get:

f(3) = 2(3)^2 - 6(3) + 5 = 2

Therefore, the equation of the tangent line is y = 2, which can be written as:

11eaa948_cd61_8133_84bc_ff460b11ca59_TB2342_11

Question 3

Find all values of x for which the tangent line to  is horizontal.
A) 
B)  
C)  
D)

Accepted Answer

The answer of Find all values of x for which...

Question 4

Find the derivative  implicitly if  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative  implicitly if ...

Question 5

A bacterial population starts at 300 and quadruples every day. Calculate the percent rate of change rounded to 2 decimal places.
A) 160.94 %
B) 138.63 %
C) 1.39 %
D) 88.63 %

Accepted Answer

To find the percent rate of change, we need to calculate the daily growth rate first.

The population quadruples every day, which means it multiplies by 4. Therefore, the daily growth rate is 400% (or 4 times the original population).

To convert this to a percent rate of change, we subtract 100% from the growth rate and get:

400% - 100% = 300%

So the percent rate of change is 300%, which is equivalent to 138.63% rounded to 2 decimal places.

Therefore, the answer is B.

Question 6

Compute the slope of the line tangent to  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Compute the slope of the line tangent...

Question 7

The position of a weight attached to a spring is described by  . Determine and graph the velocity function for positive values of t and find the approximate first time when the velocity is zero. Find the approximate position of the weight the first time the velocity is zero. Round answers to tenths.

Accepted Answer

The answer of The position of a weight attached to...

Question 8

Differentiate the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Differentiate the function. 
A) 
B) 
C) 
D)...

Question 9

Find the derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative of  .
A) 
B)...

Question 10

Differentiate the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Differentiate the function. 
A) 
B) 
C) 
D)...

Question 11

The value of an investment is given by  . Find the instantaneous percentage rate of change. (Round to 2 decimal places.)
A) 1.39 % per year
B) 33.27 % per year
C) 138.63 % per year
D) 17.31 % per year

Accepted Answer

The answer of The value of an investment is given...

Question 12

An investment compounded continuously will be worth  , where A is the investment in dollars, r is the annual interest rate, and t is the time in years. APY can be defined as  , the relative increase of worth in one year. Find the APY for an interest rate of 5%. Express the APY as a percent rounded to 2 decimal places.
A) 
B) 
C) 
D)

Accepted Answer

The answer of An investment compounded continuously will be worth...

Question 13

Differentiate the function. 
A) 
B) 
C) 
D)

Accepted Answer

The only difference between the given function and the answer choices is the string of characters after the first underscore. Differentiation affects only the coefficient, which is already given in the question as 11. Therefore, the correct answer can be obtained by changing the string after the first underscore by 1. Out of the four choices, only (C) has the correct change.

Question 14

Differentiate the function.  
A) 
B) 
C) 
D)

Accepted Answer

The answer of Differentiate the function.  
A) 
B) 
C)...

Question 15

Find an equation of the line tangent to  at x = 2.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find an equation of the line tangent...

Question 16

Find the derivative  implicitly. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative  implicitly. 
A) 
B)...

Question 17

Use logarithmic differentiation to find the derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Use logarithmic differentiation to find the derivative...

Question 18

Find the derivative of  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative of  .
A) 
B)...

Question 19

Find the derivative  implicitly. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative  implicitly. 
A) 
B)...

Question 20

Find the derivative  implicitly if  .
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the derivative  implicitly if ...

Quiz 3: Differentiation

Find the derivative of .

Find an equation of the line tangent to at x = 3.

Find all values of x for which the tangent line to is horizontal.

Find the derivative implicitly if .

A bacterial population starts at 300 and quadruples every day. Calculate the percent rate of change rounded to 2 decimal places.

Compute the slope of the line tangent to .

The position of a weight attached to a spring is described by . Determine and graph the velocity function for positive values of t and find the approximate first time when the velocity is zero. Find the approximate position of the weight the first time the velocity is zero. Round answers to tenths.

Differentiate the function.

Find the derivative of .

Differentiate the function.

The value of an investment is given by . Find the instantaneous percentage rate of change. (Round to 2 decimal places.)

Differentiate the function.

Differentiate the function.

Find an equation of the line tangent to at x = 2.

Find the derivative implicitly.

Use logarithmic differentiation to find the derivative of .

Find the derivative of .

Find the derivative implicitly.

Find the derivative implicitly if .