Science:Math Exam Resources/Courses/MATH307/December 2012/Question 01 (a)
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Question 01 (a) 

In this question we will work with polynomials of degree 3 written (a) The coefficient vector satisfies an equation of the form Aa=0 when the slopes of p(x) at x = 0 and x = 2 are zero. Write down the matrix 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 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 

Recall that we can compute the slope at a point using the derivative. 
Hint 2 

Notice that once we sub x=0 and x=2 into the derivative we will have linear equations in terms of the unknowns. How can we combine those equations to form a matrix? 
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. Slopes of p(x) = 0 at , implies When When Hence, matrix A is 