To find the equation of a line tangent to the curve  at the point , we must first find the slope of the curve at the point  by solving the derivative  at that point:

Given the slope, we can now plug the given point and the slope at that point into the slope-intercept form of the tangent line  and solve for the -intercept :

Given our slope, the chosen point, and the -intercept, we have the equation of our tangent line:

First find the slope of the tangent line by taking the derivative of the function and plugging in the x value of the given point to find the slope of the curve at that location:

So the slope of the tangent line to the curve at the given point is  .  The next step is to plug this slope into the formula for a line, along with the coordinates of the given point, to solve for the value of the y intercept of the tangent line:

We now know the slope and y intercept of the tangent line, so we can write its equation as follows:

To find the equation of a line tangent to the curve  at the point , we must first find the slope of the curve at the point  by solving the derivative  at that point:

Given the slope, we can now plug the given point and the slope at that point into the slope-intercept form of the tangent line  and solve for the -intercept :

Given our slope, the chosen point, and the -intercept, we have the equation of our tangent line:

f(x) in this case gives us a parabola. If we factor the f(x) we get:

This equation has one zero and that is at x=3. This also means we have a minimum at x=3.

The slope of a line tangent to a minimum or maximum is always 0, so our slope is zero.

The slope of the tangent line to a curve at any point is simply the slope of the curve at that point. To find the slope of the function at any point, we take the derivative:

Now we can plug in the x value of the given point, , which gives us the slope of the tangent line to the curve at that point:

To calculate the slope of a tangent line at a particular point, we need to know the slope of the curve at that point. In order to find the slope of a curve at any point, we need to calculate its derivative:

The derivative describes the slope of the curve at any point, so we need to plug in the  value of the given point    to find the slope of the tangent line at that location:

First find the derivative of the function, and then plug in the given x coordinate, which will give the slope of the function at that location. The slope of the tangent line to a curve at a given location is equal to the slope of the function at that location:

First find the derivative of the function, and then plug in the given x coordinate, which will give the slope of the function at that location. The slope of the tangent line to a curve at a given location is equal to the slope of the function at that location:

First find the derivative of the function. The slope of the tangent line to a curve at a given point is equal to the slope of the function at that point, and the derivative of a function tells us its slope at any point. Plugging the given point into the equation for the derivative, we can calculate the slope of the function, and therefore the slope of the tangent line, at that point:

Two lines are parallel if they have the same slope.  Let's go through the answer choices.

1.  and : Both slopes are 3, parallel.

2.  and : Slopes are 2 and 3, not parallel.

3.  and : We need to put these two equations into the form of  to find the slope, . 

, so the first slope is .

, so the second slope is .  These lines are perpendicular, not parallel.

4.  and : Slopes are undefined and 0, respectively, so not parallel.

5.  and : Let's again put these into the form of .

, so the first slope is .

, so the second slope is .  The lines are not parallel.