Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 03 (b)
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Question 03 (b) 

(b) Let and . Find the intercept 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 

The equation of the tangent line of the function at the value is given by . 
Hint 2 

The intercept is the value attained when . 
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. We use Hint 1 with . So the equation of the tangent line of at is We are given that and . Hence, the equation is of the tangent line becomes By Hint 2, we need to find the value of when . So we put to find Therefore, the intercept of the tangent line is . Answer: The intercept of the tangent line is . 