Science:Math Exam Resources/Courses/MATH110/April 2014/Question 01 (b)
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Question 01 (b) 

If is differentiable everywhere and has two solutions, then has at least one solution. 
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? 
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Hint 

Is there a theorem that can connect the two roots to a function’s derivative? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. True. Let be two of the roots. Then is continuous on since is differentiable everywhere, and is differentiable on . Rolle’s Theorem states that there must be a point with zero slope in the interval . 