SUMMARY
The difference quotient for the function f(x) = 1/(x-3) is calculated using the formula (f(x+h) - f(x)) / h. Substituting f(x) into the formula yields (1/(x+h-3) - 1/(x-3)) / h. Simplifying this expression correctly leads to the final result of -1 / (h(x-3)(x+h-3)). This calculation is essential for understanding the concept of derivatives in calculus.
PREREQUISITES
- Understanding of basic calculus concepts, specifically derivatives
- Familiarity with the difference quotient formula
- Knowledge of algebraic manipulation techniques
- Ability to work with rational functions
NEXT STEPS
- Study the concept of derivatives and their geometric interpretations
- Learn about limits and their role in calculus
- Explore the application of the difference quotient in finding derivatives
- Practice simplifying complex rational expressions
USEFUL FOR
Students studying calculus, educators teaching derivative concepts, and anyone looking to strengthen their understanding of the difference quotient and its applications in mathematics.