How Do You Solve the Difference Quotient for f(x) = 4 + 3x - x^2?

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SUMMARY

The discussion focuses on evaluating the difference quotient for the function f(x) = 4 + 3x - x^2. The correct formulation of the difference quotient is given by (f(3 + h) - f(3)) / h. Participants emphasize the importance of substituting x = 3 + h into the function and simplifying the expression correctly. The solution involves calculating f(3 + h) and f(3), followed by simplification to derive the final result.

PREREQUISITES
  • Understanding of difference quotients in calculus
  • Familiarity with polynomial functions
  • Ability to perform algebraic simplifications
  • Knowledge of limits and continuity concepts
NEXT STEPS
  • Practice evaluating difference quotients for various polynomial functions
  • Learn about the application of limits in calculus
  • Explore the concept of derivatives as the limit of the difference quotient
  • Study the implications of the difference quotient in real-world scenarios
USEFUL FOR

Students studying calculus, particularly those learning about difference quotients and derivatives, as well as educators seeking to clarify these concepts for their students.

nukeman
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Homework Statement



I am having trouble with a couple difference quotient questions. Here is a question I can't seem to solve.

Evaluate the difference quotient for the given funtion and simplify your answer.

f(x) = 4 + 3x - x^2 , f(3 + h) - f(3) / h




Homework Equations





The Attempt at a Solution



I have tried it a couple times, and can't seem to get it right! Any help at all would be great!
Thanks.
 
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Remember the difference quotient is:

f(x) = (f(x+h)-f(x))/h

Since you say that f(x) = 4 + 3x - x^2 plug that in for f(x) in the equation. I don't know why you would plug in f(3).
 
nukeman said:

Homework Statement



I am having trouble with a couple difference quotient questions. Here is a question I can't seem to solve.

Evaluate the difference quotient for the given funtion and simplify your answer.

f(x) = 4 + 3x - x^2 , f(3 + h) - f(3) / h




Homework Equations





The Attempt at a Solution



I have tried it a couple times, and can't seem to get it right! Any help at all would be great!
Thanks.



Should we assume you mean [f(3+h) - f(3)]/h, rather than what you wrote (which meant f(3+h) - [f(3)/h])? Anyway, if you meant the first one, what is stopping you from substituting x = 3+h into the formula and simplifying it, then substituting x = 3 and simplifying (or setting h = 0 in your first result)? When you say you can't get it right, how do know your results are wrong? Are you given an answer, and cannot seem to match it?

RGV
 

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