First find the slope of the tangent to the line by taking the derivative.

Using the Exponential Rule we get the following,

.

Then plug 1 into the equation as 1 is the point to find the slope at.

.

First find the slope of the tangent to the line by taking the derivative.

Using the Exponential Rule we get the following,

.

Then plug 1 into the equation as 1 is the point to find the slope at.

.

Calculate the derivative of by using the derivative rules. The derivative function determines the slope at any point of the original function.

The derivative is:

With the given point , . Substitute this value to the derivative function to determine the slope at that point.

The slope of the tangent line that intersects point is .

To find the slope of the tangent line of the function at the given value, evaluate the first derivative for the given value.

The first derivative is

and for this function

and plugging in the specific x value we get,

So the slope is

.

One way of finding the slope at a given point is by finding the derivative. In this case, we can take the derivative of y with respect to x, and plug in the desired value for x.

Using the exponential rule we get the following derivative,

.

Plugging in x=2 from the point 2,3 gives us the final slope,

Thus our slope at the specific point is .

Note that in this case, using the y coordinate was not necessary.

To find the slope of the tangent line of the function at the given value, evaluate the first derivative for the given value.

The first derivative is

and for this function

and plugging in the specific x value we get,

So the slope is

.

One way of finding the slope at a given point is by finding the derivative. In this case, we can take the derivative of y with respect to x, and plug in the desired value for x.

Using the exponential rule we get the following derivative,

.

Plugging in x=2 from the point 2,3 gives us the final slope,

Thus our slope at the specific point is .

Note that in this case, using the y coordinate was not necessary.

Calculate the derivative of by using the derivative rules. The derivative function determines the slope at any point of the original function.

The derivative is:

With the given point , . Substitute this value to the derivative function to determine the slope at that point.

The slope of the tangent line that intersects point is .

First, find the slope of the tangent line by taking the first derivative:

To finish determining the slope, plug in the x-value, 2:

the slope is 6

Now find the y-coordinate where x is 2 by plugging in 2 to the original equation:

To write the equation, start in point-slope form and then use algebra to get it into slope-intercept like the answer choices.

distribute the 6

add 8 to both sides

The equation of the tangent line at depends on the derivative at that point and the function value.

The derivative at that point of is

using the Power Rule

which means

The derivative is zero, so the tangent line will be horizontal.

It intersects it at since , so that line is .