Understanding Average Rate of Change

The video tutorial explains how to find the average rate of change for the function f(x) = 3x^2 - x over a closed interval from 2 to T. It begins by introducing the concept and relates it to finding the slope between two points. The tutorial then demonstrates the calculation of f(2) and f(T), followed by determining the average rate of change using these values. The process involves simplifying the expression and factoring, leading to the formula 3T + 5. An example is provided to illustrate the application of this formula for a specific interval.

What is the average rate of change of a function equivalent to?

• The slope of a tangent line

• The slope between two points

• The derivative of the function

• The integral of the function

What is the value of F(2) for the function F(x) = 3x^2 - x?

• 14

• 12

• 8

• 10

How can the function value F(2) be expressed?

• As a single number

• As a fraction

• As an ordered pair

• As a polynomial

What is the expression for F(T) in the function F(x) = 3x^2 - x?

• 3T^2 + T

• T^2 - 3T

• 3T^2 - T

• 3T - T^2

How is the change in function values calculated?

• By subtracting the function values

• By adding the function values

• By multiplying the function values

• By dividing the function values

What is the simplified expression for the average rate of change?

• 5T + 3

• 3T + 5

• 3T - 5

• 5T - 3

What is the average rate of change formula used for?

• To find the minimum value of a function

• To calculate the average rate of change over an interval

• To find the maximum value of a function

• To determine the slope of a tangent line

If T = 3, what is the average rate of change from 2 to 3?

• 12

• 18

• 14

• 16

What does the average rate of change tell us about the function?

• The function's derivative

• The function's behavior over an interval

• The function's minimum value

• The function's maximum value

For which values of T is the average rate of change formula applicable?

• T equal to 2

• T equal to 0

• T less than 2

• T greater than 2