Instantaneous Rate of Change, Average Rate of Change, and Linear Approximation - AP Calculus BC

First we must find the first derivative of the function.

Because the derivative of the exponential function is the exponential function itelf, or

and taking the derivative is a linear operation,

we have that

Now setting

Thus

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point.

For example, if , then we are looking for the value of , or the derivative of at .

Calculate

Derivative rules that will be needed here:

• Derivative of a constant is 0. For example,
• Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Find the rate of change of f(x) when x=3.

To find a rate of change, we need to find the derivative.

First, recall the following rules:

We can apply these two derivative rules to our function to get our first derivative. Then we need to plug in 3 for x and solve.

So, our answer is 105.26

First we must find the first derivative of the function.

Because the derivative of the exponential function is the exponential function itelf, or

and taking the derivative is a linear operation,

we have that

Now setting

Thus

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point.

For example, if , then we are looking for the value of , or the derivative of at .

Calculate

Derivative rules that will be needed here:

• Derivative of a constant is 0. For example,
• Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Find the rate of change of f(x) when x=3.

To find a rate of change, we need to find the derivative.

First, recall the following rules:

We can apply these two derivative rules to our function to get our first derivative. Then we need to plug in 3 for x and solve.

So, our answer is 105.26

First we must find the first derivative of the function.

Because the derivative of the exponential function is the exponential function itelf, or

and taking the derivative is a linear operation,

we have that

Now setting

Thus

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point.

For example, if , then we are looking for the value of , or the derivative of at .

Calculate

Derivative rules that will be needed here:

• Derivative of a constant is 0. For example,
• Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Find the rate of change of f(x) when x=3.

To find a rate of change, we need to find the derivative.

First, recall the following rules:

We can apply these two derivative rules to our function to get our first derivative. Then we need to plug in 3 for x and solve.

So, our answer is 105.26

First we must find the first derivative of the function.

Because the derivative of the exponential function is the exponential function itelf, or

and taking the derivative is a linear operation,

we have that

Now setting

Thus

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point.

For example, if , then we are looking for the value of , or the derivative of at .

Calculate

Derivative rules that will be needed here:

• Derivative of a constant is 0. For example,
• Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Find the rate of change of f(x) when x=3.

To find a rate of change, we need to find the derivative.

First, recall the following rules:

We can apply these two derivative rules to our function to get our first derivative. Then we need to plug in 3 for x and solve.

So, our answer is 105.26

First we must find the first derivative of the function.

Because the derivative of the exponential function is the exponential function itelf, or

and taking the derivative is a linear operation,

we have that

Now setting

Thus

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point.

For example, if , then we are looking for the value of , or the derivative of at .

Calculate

Derivative rules that will be needed here:

• Derivative of a constant is 0. For example,
• Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Find the rate of change of f(x) when x=3.

To find a rate of change, we need to find the derivative.

First, recall the following rules:

We can apply these two derivative rules to our function to get our first derivative. Then we need to plug in 3 for x and solve.

So, our answer is 105.26

First we must find the first derivative of the function.

Because the derivative of the exponential function is the exponential function itelf, or

and taking the derivative is a linear operation,

we have that

Now setting

Thus

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point.

For example, if , then we are looking for the value of , or the derivative of at .

Calculate

Derivative rules that will be needed here:

• Derivative of a constant is 0. For example,
• Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate

Find the rate of change of f(x) when x=3.

To find a rate of change, we need to find the derivative.

First, recall the following rules:

We can apply these two derivative rules to our function to get our first derivative. Then we need to plug in 3 for x and solve.

So, our answer is 105.26

First we must find the first derivative of the function.

Because the derivative of the exponential function is the exponential function itelf, or

and taking the derivative is a linear operation,

we have that

Now setting

Thus

There are 2 steps to solving this problem.

First, take the derivative of .

Then, replace the value of x with the given point.

For example, if , then we are looking for the value of , or the derivative of at .

Calculate

Derivative rules that will be needed here:

• Derivative of a constant is 0. For example,
• Taking a derivative on a term, or using the power rule, can be done by doing the following:

Then, plug in the value of x and evaluate