Science:Math Exam Resources/Courses/MATH100/December 2012/Question 01 (a)
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Question 01 (a) 

ShortAnswer Questions. Questions 14 are shortanswer questions. Put your answers in the boxes provided. Simplify your answers as much as possible, and show your work. Each question is worth 3 marks, but not all questions are of equal difficulty.

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 

We wish to find a function with derivative as given. So what function gives a derivative of ? What about for ? Lastly, don't forget that adding a constant to the function also gives an antiderivative. Use the information ƒ(0) = 0 to find this constant. 
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. Since and , we have that the function given by where C is any constant are functions that have the given derivative. Since we are also given that , we plug this information in to see that . Isolating for C gives . Thus the required function is given by 