Question 1

For  find all real numbers a and b such that  exists.
A)  b any real number
B)  
C)  b any real number
D)

Accepted Answer

The answer of For  find all real numbers a...

Question 2

Below is a graph of  . Sketch a graph of  .

Accepted Answer

The answer of Below is a graph of  ....

Question 3

Find the derivative of f(x) = x² + 3x + 2. A) x + 3 B) 2x² + 2 C) 2x + 3 D) -2x - 3

Accepted Answer

The derivative of $f(x) = x^{12} + 3x + 2$ is found by applying the power rule and the sum rule of differentiation. The derivative of $x^{12}$ is $12x^{11}$, the derivative of $3x$ is $3$, and the derivative of a constant (2) is 0. Therefore, the derivative $f'(x) = 12x^{11} + 3$. However, none of the provided options correctly matches this derivative, suggesting a potential misunderstanding or typo in the question or options. Based on the options given, option C, "2x + 3," is the closest to a standard derivative form, but it does not accurately represent the derivative of the given function.

Question 4

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

Accepted Answer

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

Question 5

Sketch the graph of a function with the following properties:      and 
A) 
B) 
C) 
D)

Accepted Answer

The graph has a period of 2 and an amplitude of 3. It starts at (0,2) and has a vertical shift of 5. Choice B corresponds to the function y = 3sin(πx) + 5, which has all of these properties.

Question 6

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

Accepted Answer

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

Question 7

Below is a graph of  . Sketch a plausible graph of a continuous function  .

Accepted Answer

The answer of Below is a graph of  ....

Question 8

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

Accepted Answer

The given expression is a hexadecimal number written in the scientific notation, where the base is 16 and the exponent is represented by "_TB2342_11". To take the derivative of this expression, we need to treat it as a constant value, as the hexadecimal notation does not allow for algebraic manipulation. Taking the derivative of a constant value gives us zero. 
Therefore, the only option that ends with "_99ed_" (indicating a value of zero) is B.

Question 9

Below is a graph of  . Sketch a plausible graph of a continuous function  .

Accepted Answer

The answer of Below is a graph of  ....

Question 10

Below is a graph of  . Sketch a graph of  .

Accepted Answer

The answer of Below is a graph of  ....

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Use the distances f(t) to estimate the velocity at t = 2.2. (Round to 2 decimal places.) 
A) -2250.00
B) 29.09
C) 22.50
D) 25.00

Accepted Answer

The answer of Use the distances f(t) to estimate the...

Question 14

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

Accepted Answer

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

Question 15

The table below gives the position s(t) for a car beginning at a point and returning 5 hours later. Estimate the velocity v(t) at two points around the third hour.

Accepted Answer

The answer of The table below gives the position s(t)...

Question 16

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer. 
A) 32 ft/sec
B) 36 ft/sec
C) 26 ft/sec
D) 28 ft/sec

Accepted Answer

The answer of Suppose a sprinter reaches the following distances...

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Numerically estimate the derivative  for 
A) 0
B) 1
C) 3
D) 5

Accepted Answer

The answer of Numerically estimate the derivative  for 
A)...

Question 20

Compute the right-hand derivative  and the left-hand derivative  . 
A)  , 
B)  , 
C)  , 
D)  ,

Accepted Answer

The answer of Compute the right-hand derivative  and the...

Quiz 3: Differentiation

For find all real numbers a and b such that exists.

Below is a graph of . Sketch a graph of .

Find the derivative of f(x) = x2 + 3x + 2.

Differentiate the function.

Sketch the graph of a function with the following properties: and

Find the second derivative of .

Below is a graph of . Sketch a plausible graph of a continuous function .

Find the derivative of .

Below is a graph of . Sketch a plausible graph of a continuous function .

Below is a graph of . Sketch a graph of .

Differentiate the function.

Find the derivative of .

Use the distances f(t) to estimate the velocity at t = 2.2. (Round to 2 decimal places.)

Find the third derivative of .

The table below gives the position s(t) for a car beginning at a point and returning 5 hours later. Estimate the velocity v(t) at two points around the third hour.

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer.

Differentiate the function.

Find the derivative of .

Numerically estimate the derivative for

Compute the right-hand derivative and the left-hand derivative .

Find the derivative of f(x) = x² + 3x + 2.