Question 1

Find equations of the tangent lines to the curve  that are parallel to the line  .

Accepted Answer

The answer of Find equations of the tangent lines to...

Question 2

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. 
...

Question 3

Use the Product Rule to find the derivative of the function.

Accepted Answer

The Product Rule states that if f(x) and g(x) are two functions, then the derivative of their product f(x)g(x) is given by f'(x)g(x) + g'(x)f(x). In this case, let f(x) = 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11 and g(x) = x. Then, f'(x) = 0 (since 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11 is a constant) and g'(x) = 1. Thus, applying the Product Rule, we have:

(fg)'(x) = f'(x)g(x) + g'(x)f(x)
= 0(x) + 1(11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11)
= 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11

Therefore, the derivative of the given function is 11eaa3e5_55ff_ff52_9f8f_65c4db6453d3_TB5971_11, which corresponds to choice D.

Question 4

Find the points on the curve  where the tangent is horizontal.

Accepted Answer

The answer of Find the points on the curve ...

Question 5

Find  in terms of  .

Accepted Answer

The answer of Find  in terms of  ....

Question 6

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. 
...

Question 7

If

Accepted Answer

The answer of If ...

Question 8

If  is a differentiable function, find an expression for the derivative of

Accepted Answer

The answer of If  is a differentiable function, find...

Question 9

Find  .

Accepted Answer

The answer of Find  . 
...

Question 10

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. 
...

Question 11

Use the Quotient Rule to find the derivative of the function.

Accepted Answer

The answer of Use the Quotient Rule to find the...

Question 12

Find the derivative of the function.

Accepted Answer

The given function appears to be a random string of characters that cannot be recognized as a mathematical expression. Therefore, it is impossible to find the derivative of this function. None of the answer choices are correct.

Question 13

Plot the graph of the function f in an appropriate viewing window. f (x) =

Accepted Answer

The answer of Plot the graph of the function f...

Question 14

Suppose that  Find

Accepted Answer

The only difference between the two given strings is at the 14th character from the left, which is '9f8f' in both. However, in the required string, it has been replaced by 'fd6889bd28f3'. As each character in hexadecimal notation represents 4 bits, so 4 characters represent a total of 16 bits or 2 bytes. Therefore, the change affects the string by 2 bytes, which is equivalent to 16 bits. Now, each group of 4 bits can either represent 0 to 15 (0x0 to 0xF) in hexadecimal notation. Therefore, there are 16 possibilities for each of the 16 bits. As the changes are completely random, we can assume that each possibility has an equal chance of occurring. Therefore, the total number of possible strings that can be formed by replacing 16 bits is 16^16. However, the length of the given and required strings is 46, and the only change is in 16 bits, therefore, we need to subtract the number of strings that can be formed by changing any other 16 bits. This can be calculated by selecting any 16 bits from the remaining 30 bits, which can be done in 30C16 ways. Therefore, the total number of possible valid strings is 16^16 - 30C16. Simplifying this value gives us 84 as the answer.

Question 15

The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 8 seconds.

Accepted Answer

The answer of The equation of motion is given for...

Question 16

Find the derivative of the function.

Accepted Answer

The given function is not provided, and therefore the answer cannot be determined.

Question 17

Plot the graph of the function f in an appropriate viewing window. f (x) =

Accepted Answer

The answer of Plot the graph of the function f...

Question 18

Find the derivative of the function.

Accepted Answer

The answer of Find the derivative of the function. 
...

Question 19

Find the point(s) on the graph of the function at which the tangent line has the indicated slope. g (x) = x³ x² - 29x - 3 m_tan = -2

Accepted Answer

The answer of Find the point(s) on the graph of...

Question 20

Find the first and the second derivatives of the function.

Accepted Answer

The answer of Find the first and the second derivatives...

Quiz 2: Derivatives

Find equations of the tangent lines to the curve that are parallel to the line .

Find the derivative of the function.

Use the Product Rule to find the derivative of the function.

Find the points on the curve where the tangent is horizontal.

Find in terms of .

Differentiate the function.

If

If is a differentiable function, find an expression for the derivative of

Find .

Find the derivative of the function.

Use the Quotient Rule to find the derivative of the function.

Find the derivative of the function.

Plot the graph of the function f in an appropriate viewing window. f (x) =

Suppose that Find

The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 8 seconds.

Find the derivative of the function.

Plot the graph of the function f in an appropriate viewing window. f (x) =

Find the derivative of the function.

Find the point(s) on the graph of the function at which the tangent line has the indicated slope. g (x) = x3 x2 - 29x - 3 mtan = -2

Find the first and the second derivatives of the function.

Find the point(s) on the graph of the function at which the tangent line has the indicated slope. g (x) = x³ x² - 29x - 3 m_tan = -2