AP Calculus AB : Derivatives

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

Example Question #711 : Derivatives

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Correct answer:

Explanation:

Example Question #712 : Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #711 : Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #712 : Derivatives

Possible Answers:

Correct answer:

Explanation:

Example Question #713 : Derivatives

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Correct answer:

Explanation:

Example Question #714 : Derivatives

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Example Question #715 : Derivatives

The motion of a particle on Mars at any time  can be represented by the following equation:

Find the velocity of the particle at 

Possible Answers:

Correct answer:

Explanation:

We can represent the velocity as the instantaneous rate of change of a particles motion, that is . We solve the problem by taking the derivative of the function that describes the particles motion with respect to time

We then evaluate the velocity equation at the specified time, which in this case was 

Example Question #716 : Derivatives

A particles position at any point in time can be modeled by the following equation

Find the velocity of the particle when 

Possible Answers:

Correct answer:

Explanation:

The velocity is the instantaneous rate of change of the particles position with respect to time (), so by taking the derivative of the function we can find the particles velocity ant any point in time

Evaluating at the time we specified in the problem statement, we get

Example Question #719 : Derivatives

The amount of bacteria in a dish (as a function of time) is modeled according to the following expression:

At what time will the amount of bacteria be growing at a rate of 38?

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To determine the rate of change of the amount of bacteria at a specific time, we must take the derivative of the function:

The derivative was found using the following rules:

Now, we are asked to find the time corresponding to a certain rate of growth of the bacteria. This is the output of the derivative function, from a certain time input into the function. So, we must solve for the time that gets us 38 as our output:

 

Example Question #717 : Derivatives

An electron in motion can be described by the following equation, which gives its position at any point in time

Find the speed of the electron when 

Possible Answers:

Correct answer:

Explanation:

To find the velocity of the electron, we take the derivative of its position equation. Velocity is the instantaneous rate of change ofposition with respect to time, which we will evaluate at a specified time

Evaluating when 

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