At what point(s) on the given curve is the tangent line horizontal?

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SUMMARY

The discussion confirms that the tangent line is horizontal at points of local maxima and minima on a given curve. Participants emphasize the importance of self-confidence in problem-solving and suggest using tools like WolframAlpha for verifying numerical solutions. The conversation highlights the value of peer support in mathematical learning and problem-solving.

PREREQUISITES
  • Understanding of calculus concepts such as local maxima and minima
  • Familiarity with tangent lines and their properties
  • Basic knowledge of using computational tools like WolframAlpha
  • Confidence in mathematical problem-solving skills
NEXT STEPS
  • Explore the concept of derivatives and their role in identifying local extrema
  • Learn how to use WolframAlpha for calculus problems
  • Study graphical interpretations of functions and their tangent lines
  • Investigate the implications of horizontal tangents in real-world applications
USEFUL FOR

Students and educators in mathematics, particularly those studying calculus, as well as anyone seeking to enhance their problem-solving confidence and verify solutions using computational tools.

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Homework Statement
Can someone check to see if my two points are accurate?
Relevant Equations
n/a
IMG_4215.jpg
 
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Yes, of course it is! You have posted several questions in which you have given detailed solutions. Wonderful! My only question is why you would feel the need to ask!
 
HallsofIvy said:
Yes, of course it is! You have posted several questions in which you have given detailed solutions. Wonderful! My only question is why you would feel the need to ask!
It's always relieving and reassuring when I get a heads up from brilliant tutors online :)
Thank you!
 
If you just want a check of a numerical solution, you could try WolframAlpha.
Local maximum:
gif&s=25.gif

Local minimum:
gif&s=25.gif
 
You should have more confidence in your own "brilliance".
 
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