Average Value of a Function
Definition
The average value of a function over an interval is the total change in the function divided by the length of the interval.
Analogy
Imagine you are driving a car and you want to know your average speed for a trip. You would calculate it by dividing the total distance traveled by the time it took. Similarly, finding the average value of a function is like finding its average "speed" over an interval.
Related terms
Particle Motion: Refers to the movement of an object along a path. It can be described using functions that represent position, velocity, and acceleration.
Net Change: Represents the overall difference or total amount of change in a quantity over an interval. It can be calculated by subtracting initial value from final value.
Definite Integral: In calculus, it represents the signed area between a curve and x-axis over an interval. It can also be used to find average values and net changes.
"Average Value of a Function" appears in:
Additional resources (3)
Practice Questions (4)
Which of the following represents the average value of a function f(x) over the interval [a, b]?
Which of the following represents the average value of a function f(x) over the interval [a, b]?
How do you find the average value of a function over an interval?
If the average value of a function over an interval is equal to the function-value at a specific point within the interval, what can we imply about the function?
Resources
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