Science:Math Exam Resources/Courses/MATH110/April 2018/Question 01 (c)
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Question 01 (c) 

Find the equation of the tangent line to at . 
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 

To find the equation of a line, you need to find two things: the slope of the line and a point contained on the line. 
Hint 2 

The slope of the tangent line to at is equal to . 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. The first step will be to find the slope of the tangent line to at , which is given by the derivative of at . Using the power rule, we see that the derivative of is , so the derivative of at is . We want to use the slopepoint formula to find the equation of the tangent line. Having found the slope, it remains to find a point contained on the line. The tangent line must pass through at , so it must contain the point . Now the slopepoint formula tells us that the equation of the tangent line is given by . After rearranging, we get the equation . Answer: The equation of the tangent line at is . 