(Q18.) Sample 3 GCC Math 101/120 Common Final Intermediate Algebra

TL;DR

Learn how to simplify an expression using the difference quotient, step-by-step.

Transcript

okay for number 18 we are going to find and simplifi this expression F ofx + H minus f of x all over H and we have the function f ofx is = to X2 + 2x - 3 this is called a difference quent and I'll show you guys how to work this out and notice that this formula right here it requires us to find what's f ofx plus h so that's the first step we have to... Read More

Key Insights

• ☠️ The difference quotient is a tool used in calculus to find the average rate of change or the derivative of a function.
• ☺️ When finding F(x + H) using the given function, substitute x + H into each term separately.
• 🍉 Simplification involves multiplying out terms, combining like terms, and canceling out common factors.

Questions & Answers

Q: What is the purpose of the difference quotient?

The difference quotient is used to find the average rate of change of a function over a small interval, or to find the derivative of a function.

Q: How do you find F(x + H) using the given function?

To find F(x + H), substitute x + H into each term of the given function and simplify the expression.

Q: Can you explain the process of simplifying the expression step-by-step?

First, multiply out the terms (x + H) * (x + H) to get x² + 2xH + H². Then combine like terms and cancel out common factors to simplify the expression.

Q: What is the final answer of the expression after simplification?

The final answer is 2x + H + 2.

Summary & Key Takeaways

• The video teaches how to simplify the expression F(x + H) - F(x) / H using the difference quotient.

• Start by finding F(x + H) by substituting x + H into the given function.

• Simplify the expression by combining like terms and canceling out common factors.