Science:Math Exam Resources/Courses/MATH110/April 2018/Question 02 (d)
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Question 02 (d) 

Consider a function whose graph is showed below. On which of the following intervals does the Mean Value Theorem (MVT) apply to ? Select all that apply. If the theorem applies, give a reasonable estimate of the number in the given interval that satisfies the conclusion of the theorem. (a) , and the number that satisfies the conclusion of MVT is ____

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 

For the MVT to apply on an interval , the function must be continuous on the closed interval and differentiable on the open interval . 
Hint 2 

The number is the coordinate at which the average slope of on the interval is attained. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The MVT does not apply for (a), since the function is undefined (and thus not continuous) at the point . The MVT does apply for (b), since the function is continuous on the closed interval and differentiable on the open interval . The average slope of on this interval is , so a reasonable estimate for would be something around since the tangent line to at seems to have slope around . The MVT does apply for (c), since the function is continuous on the closed interval and differentiable on the open interval . The average slope of on this interval is , so a reasonable estimate for would be since the tangent line to at seems to have slope equal to . The MVT does not apply for (d), since the function is not differentiable at the point which lies within the open interval . Answer: The correct answers are . 