Science:Math Exam Resources/Courses/MATH110/December 2013/Question 02
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Question 02 

Find the equations of the two tangent lines to the curve that are parallel to the line x  2y = 2. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Remember that the derivative of a function at a point is equal to the slope of the tangent line at that point. First find the slope of the given line by changing this equation to the form 
Hint 2 

Once you find the slope of the given line, set it equal to the derivative of the given function, which we find using the quotient rule. 
Hint 3 

Following the first two hints, we should now have two xvalues. Plug these values back into the function definition to find the yvalues. After this, you now have the points and the slope of the two lines you need to find to solve the question. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We first recognise that parallel means that the slopes must be equal. Rearranging the equation, we get:
So that means we are looking for points along the curve with slope equal to . To get those points, we need the derivative of the curve:
Using the quotient rule, we get:
So that means:
We are interested in points where the derivative is
This means we have to tackle two potential values. At , we have:
At , we have:
So that means the tangent lines are are looking for are: for .
and for
