Science:Math Exam Resources/Courses/MATH100/December 2015/Question 05 (b)
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Question 05 (b) 

Let be a function differentiable at and let . The line tangent to the curve at has slope 2 while the line tangent to the curve at has slope 5. What is ? 
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 

For arbitrary given function , how to interpret the statement that the line tangent to the curve at has slope ? 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. The line tangent to the curve at has slope 2 means . Similarly, since the line tangent to the curve at has slope 5, we have . Then, using the product rule with , , hence at we have . Therefore, the answer is . 