How to Find the Difference Quotient (f(x + h) - f(x))/h) for f(x) = 1/x

TL;DR

Compute the difference quotient for 1/X step by step to simplify the expression.

Transcript

hi everyone in this video we're going to compute this expression here this is called the difference quotient so the function is 1 over X and all we have to do is compute this and carefully simplify it ok let's go through it really carefully so solution so I like to start these problems by writing down the formula so let's do that first so we have f... Read More

Key Insights

• ❓ Understanding the difference quotient concept is essential in calculus.
• 😑 Careful evaluation and simplification techniques are crucial in solving mathematical expressions.
• 🦻 Keeping track of parentheses and applying reciprocal properties aid in deriving accurate final answers.

Questions & Answers

Q: What is the first step in computing the difference quotient for 1/X?

The first step is to write down the formula which involves f(X + h) - f(X) divided by h, where f(X) is 1/X.

Q: How do you proceed after plugging in the values for f(X + h) and f(X)?

After substituting 1/X+h and 1/X respectively, you simplify the expression by finding the least common denominator and carefully simplifying the fractions.

Q: Why is it important to keep parentheses while simplifying fractions over fractions?

Keeping parentheses ensures the correct grouping of terms, especially when dealing with fractions over fractions to avoid errors in the simplification process.

Q: How is the final answer of -1/(X + h) * X obtained from the simplified expression?

By applying the reciprocal property when dividing by h, the final expression cancels out the terms to result in -1/(X + h) * X.

Summary & Key Takeaways

• The video explains how to compute the difference quotient for the function 1/X.

• It demonstrates step by step the process of simplifying the expression through careful evaluation.

• By using the formula and simplifying techniques, the final answer is derived as -1/(X + h) * X.