Question 1

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

Accepted Answer

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

Question 2

Below is a graph of  . Sketch a graph of  .

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

Question 3

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

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.

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The answer of Differentiate the function. 
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Question 5

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

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  .

Accepted Answer

The answer of Find the second derivative of  .
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Question 7

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

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

Question 8

Find the derivative of  .

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  .

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

Question 10

Below is a graph of  . Sketch a graph of  .

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

Question 11

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. 
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Question 12

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
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Question 13

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

Accepted Answer

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

Question 14

Find the third derivative of  .

Accepted Answer

The answer of Find the third derivative of  .
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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.

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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.

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

Question 17

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. 
...

Question 18

Find the derivative of  .

Accepted Answer

The answer of Find the derivative of  .
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Question 19

Numerically estimate the derivative  for

Accepted Answer

The answer of Numerically estimate the derivative  for 
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Question 20

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

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.