<h2>
Part 1.</h2>
Answer: 
The limit of the difference quotient is simply the derivative, so we can express this as follows:

So our function is:

Taking the derivative, we have:

So the correct option is:

<h2>Part 2.</h2>
Answer: 
The equation of the line that passes through the same point can be found as:

Where
, so we need to find
. Plug in that x-value in the function we have:

And the slope is:

Then, the equation of the line is:

<h2 /><h2>Part 3.</h2>
Answer: Shown below
As you can see below, the graph of the function of
is continuous. This is so because we have plotted a polynomial function whose domain is the set of all real numbers. So the function is defined at the point
, so the derivative exists at this point, hence we can calculate a tangent line there. In conclusion, we get the graph shown below. The blue line is the tangent line while the red curve is the graph of 