Verifying the Correctness of Your Answer

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SUMMARY

The discussion centers on verifying the correctness of mathematical expressions, specifically the use of logical operators in defining intervals. The correct terminology emphasizes using "OR" instead of "AND" when describing the union of intervals, as indicated by the notation ##\cup## for unions and ##\cap## for intersections. The intervals discussed include ##[-4,-2]## and ##[4,6]##, with a focus on the behavior of functions around asymptotes, particularly at ##x=-6##. The importance of including all relevant intervals, such as ##(6,7]##, is also highlighted.

PREREQUISITES
  • Understanding of set notation and interval notation
  • Familiarity with mathematical concepts of increasing and decreasing functions
  • Knowledge of asymptotes and their implications on function definitions
  • Basic proficiency in logical operators (AND, OR) in mathematical contexts
NEXT STEPS
  • Study the properties of unions and intersections in set theory
  • Learn about the behavior of functions near asymptotes
  • Explore interval notation and its applications in calculus
  • Review examples of increasing and decreasing functions with various intervals
USEFUL FOR

Students in mathematics, educators teaching calculus concepts, and anyone involved in verifying mathematical expressions and functions.

angela107
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Homework Statement
Given the following graph, what are the intervals where the function is increasing, decreasing, or constant?
Relevant Equations
n/a
Screen Shot 2020-05-28 at 12.47.36 PM.png

Screen Shot 2020-05-28 at 2.32.42 PM.png

Is this answer correct?
 
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I see what you mean, but you should write OR instead of AND. The word AND corresponds to ##\cap## while OR corresponds to ##\cup##, which is what you need here.

So, to be totally clear, rather write: Increasing on ##[-4,-2]\cup [4,6]## and similarly for decreasing.
 
I'm not really sure, but if in ##x=-6## there is an asymptote, then the function is not defined in ##\left(-\infty,-6\right]##
 
What happened to (6,7]?
 
haruspex said:
What happened to (6,7]?
that is also increasing.
 
angela107 said:
that is also increasing.
Sure, just pointing out that you omitted it from your answer.
 
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Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
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