Determining the Difference Quotient

The video tutorial explains how to evaluate a function F(x) = x^2 - x + 1 using the difference quotient. It covers evaluating the function for 2 + H and 2, and then simplifying the difference quotient. The final result is expressed as H + 3, with the constraint that H cannot be zero. The tutorial provides a step-by-step approach to understanding the process, preparing students for more advanced calculus concepts.

What is the initial function F(x) introduced in the video?

• F(x) = x^2 + x + 1

• F(x) = x^2 - x + 1

• F(x) = x^2 + x - 1

• F(x) = x^2 - x - 1

What is the expression obtained after evaluating F(2 + h)?

• h^2 + 2h + 4

• h^2 + 3h + 3

• h^2 + 5h + 2

• h^2 + 4h + 5

What is the value of F(2) as calculated in the video?

• 4

• 2

• 5

• 3

What is the final simplified form of the difference quotient?

• h + 5

• h + 2

• h + 3

• h + 4

Why is it important that h cannot be equal to 0 in the difference quotient?

• To avoid division by zero

• To simplify the expression

• To ensure the function is continuous

• To make the function differentiable