#36. Find the Difference Quotient (f(x + h) - f(x))/h for the Function f(x) = 2x^2 - 5x | Summary and Q&A

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June 22, 2018
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#36. Find the Difference Quotient (f(x + h) - f(x))/h for the Function f(x) = 2x^2 - 5x

TL;DR

Learn how to find the difference quotient for a quadratic function by evaluating f(X+h) and simplifying the expression.

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Key Insights

  • ☠️ The difference quotient is used to find the average rate of change of a function over a small interval.
  • ❓ Substituting (X+h) for X in a function is a common technique in calculus and algebra.
  • 😑 Simplifying the expression involves expanding and combining like terms.

Transcript

let's workout problem number 36 find the difference quotient for the function below simplify your answer as much as possible so the function given is f of X equals 2x squared minus 5x and we have to find the difference quotient for this function so the difference quotient is f of X plus h minus f of X and it's all over H ok it's the first thing we ... Read More

Questions & Answers

Q: What is the first step to finding the difference quotient for a quadratic function?

The first step is to evaluate f(X+h) by replacing all instances of X in the function with (X+h).

Q: Why is it important to use parentheses when substituting (X+h) into the quadratic function?

It is important to use parentheses to properly distribute and simplify the expression, ensuring accurate results.

Q: How do you simplify the expression after evaluating f(X+h) and f(X)?

After evaluating, you expand and simplify the terms, combining like terms and distributing any coefficients.

Q: What is the final answer for the difference quotient of the given quadratic function?

The final answer is 4x + 2h - 5, which is obtained after simplifying the expression and canceling out the duplicate terms.

Summary & Key Takeaways

  • The content teaches how to find the difference quotient for a given quadratic function.

  • It involves substituting (X+h) for X in the function, simplifying the expression, and dividing it by h.

  • The final answer is 4x + 2h - 5.

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