Science:Math Exam Resources/Courses/MATH102/December 2015/Question 10 (a)
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 • Q7 • Q8 • Q9 • Q10 (a) • Q10 (b) • Q11 • Q12 • Q13 • Q14 (a) • Q14 (b) • Q15 • Q16 • Q17 • Q18 (a) • Q18 (b) • Q18 (c) • Q18 (d) • Q19 (a) • Q19 (b) • Q19 (c) • Q19 (d) • Q19 (e) •
Question 10 (a) 

Consider the function (solid curve) and its tangent line at (dashed). The graph of is symmetric about . Calculate the quantities below. (a) 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Recall the definition of the derivative. 
Checking a solution serves two purposes: helping you if, after having used the hint, 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. By the definition of a derivative, the given quantity equals to ;
To get , it is enough to find the slope of the tangent line of the function at . From the graph, we can see that the tangent line passes though the two points and , so that its slope is . Therefore, we have 