Find Values of x with Prescribed Slope

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SUMMARY

The discussion centers on the mathematical concept of finding values of x where a function has a prescribed slope, particularly in the context of differentiation. Participants suggest that this involves identifying points where the function is differentiable and where it is not. Additionally, there is a possibility that "prescribed slope" refers to a specific slope value, such as 5, where one must determine where the derivative of the function equals that value. Clarification from the professor is recommended for precise understanding.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically differentiation.
  • Familiarity with the definition of differentiability in functions.
  • Knowledge of how to compute derivatives of functions.
  • Ability to interpret mathematical terminology and notation.
NEXT STEPS
  • Review the definition and properties of differentiable functions.
  • Learn how to compute derivatives using rules of differentiation.
  • Study examples of finding critical points where the derivative equals a specific value.
  • Explore the implications of non-differentiable points in function analysis.
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Students preparing for calculus exams, educators teaching differentiation, and anyone interested in understanding the behavior of functions in relation to their slopes.

BrownianMan
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"Prescribed slope"

Ok, so the prof gave us a list of topics and sample questions to focus on for the midterm. This is one of them:

Find all values of x where the graph of a given function has a prescribed slope.

I take this to mean, "find all the values of x where the given function is differentiable," or just find the values of x where it is not differentiable and say that everywhere else, it is differentiable. Is this correct?
 
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Sounds reasonable to me, although "prescribed slope" is not a term I'm familiar with. You should get clarification from your prof.
 


Another interpretation could be that he will prescribe the slope, e.g. 5, and you will need to find where the derivative equals that. I agree that you should get clarification.
 

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