Science:Math Exam Resources/Courses/MATH110/December 2014/Question 03 (e)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q3 (e) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q10 • Q11 •
Question 03 (e) 

Now consider the function where and are constants. Find values for and such that is differentiable 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 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 that if is not continuous at , then it is not differentiable at the same point. Therefore, to be differentiable at , must be continuous at the point first. 
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. As we mentioned in the Hint, must be continuous at . This means . Since we have and , for the continuity at , we need . On the other hand, the slope of also should be matched. i.e., . The lefthand side can be evaluated by , while the right hand side becomes . Therefore, we get and plugging this back to the equation , we obtain . Answer: 