Science:Math Exam Resources/Courses/MATH110/December 2010/Question 01 (c)
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Question 01 (c) 

Determine whether this statement is true. If it is, explain why; if not, give a counterexample. If , then 
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 

Can you think of two functions which are different, but have the same derivative? What parts of a function can disappear after taking the derivative? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The statement is false. If we have two functions that only differ by a constant, when we take the derivative the constant will disappear, making the derivatives equal. However the original functions were not equal to start with. A simple concrete example would be: suppose and . Even though their derivatives are equal, the original functions aren't equal. More generally, if and where is a differentiable function, then but . 