# AP Calculus AB : Derivatives

## Example Questions

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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

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

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?

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