# Calculus 1 : How to find rate of change

## Example Questions

### Example Question #791 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 8 and a rate of growth of 33?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rates of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now, with the rate equation known, we can solve for the rate of change of the surface area with what we know about the cube, namely that its sides have a length of 8 and a rate of growth of 33:

### Example Question #881 : Rate

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 7 and a rate of growth of 34?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 7 and a rate of growth of 34:

### Example Question #791 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 6 and a rate of growth of 35?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 6 and a rate of growth of 35:

### Example Question #791 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 5 and a rate of growth of 36?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 5 and a rate of growth of 36:

### Example Question #792 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 4 and a rate of growth of 37?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 4 and a rate of growth of 37:

### Example Question #793 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 3 and a rate of growth of 38?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 3 and a rate of growth of 38:

### Example Question #795 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 2 and a rate of growth of 39?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 2 and a rate of growth of 39:

### Example Question #796 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 1 and a rate of growth of 40?

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area in terms of the length of its sides:

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 1 and a rate of growth of 40:

### Example Question #799 : How To Find Rate Of Change

Find the rate of change of  from

Explanation:

To do rate of change , remember it is equivalent to finding slope.

### Example Question #797 : How To Find Rate Of Change

The position of a car is defined by the equation .  What is the average velocity of the car between  and ?