Science:Math Exam Resources/Courses/MATH105/April 2011/Question 09 (b)
• Q1 (a) • Q1 (b) • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 • Q7 • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) • Q9 (f) • Q9 (g) •
Question 09 (b) 

Each of the shortanswer questions below is worth 5 points. Put your answer in the box provided and show your work. No credit will be given for the answer without the correct accompanying work. What is the slope of the curve
at the point 
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 

Apply the fundamental theorem of calculus to the integral. i.e: where F'(x) = f(x). 
Hint 2 

Consider the first hint. Can you take the derivative of with respect to where is a function of ? 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. To evaluate the slope of the curve at , we let and evaluate . By the fundamental theorem of calculus, we know that where is the antiderivative of the integrand (i.e: ). Taking the derivative with respect to , we find So the slope of the curve at is 2. 