study guides for every class

that actually explain what's on your next test

Interval

from class:

AP Calculus AB/BC

Definition

An interval represents a range or segment on the number line between two points. It includes all numbers within those endpoints and may be open (excluding endpoints) or closed (including endpoints).

"Interval" also found in:

Practice Questions (20+)

What happens if a function is not continuous over an interval?
Consider the function f(x) = 2x^3 + 5x^2 - 3x. What is the average rate of change of f(x) over the interval [1, 3]?
The function f(x) = 2x + 3 represents the position of an object at time x. What is the average rate of change of the object's position over the interval [2, 5]?
Consider the function f(x) = x^3 + 2x - 4. Find the slope of the secant line passing through the interval [-1, 2]?
The temperature T (in degrees Celsius) of a cup of coffee after t minutes is given by the function T(t) = 2t + 20. What is the average rate of change of the temperature of the coffee over the interval [5, 10]?
If a function is differentiable on the interval (a, b), which of the following must be true?
Consider the function f(x) = x^2 on the interval [-2, 2]. Which of the following is guaranteed by the Mean Value Theorem for this function?
If the first derivative of a function is zero for an interval, what can be said about the behavior of the function on that interval?
If the second derivative of a function is zero for an interval, what can be said about the behavior of the function on that interval?
Which of the following is true for the definite integral of a constant function over a given interval?
Which of the following is true regarding the definite integral of a function over an interval?
Which of the following is true for the definite integral of a non-negative function over a given interval?
If the second derivative is zero for all x-values in a given interval, then:
The integral, $\int_{0}^{4} (3 + 4t) , dt$ represents the accumulation of the function $(3 + 4t)$ over the interval $[0, 4]$. Evaluate the integral.
The derivative of an integrally-defined function $h(x)$ is given by $f(x)$, in other words h(x) = ∫f(x) dx. If $f(x)$ is positive on an interval $(a, b)$, what can be said about the behavior of $h(x)$ on that interval?
If the graph of the first derivative $f(x)$ of an integrally-defined function $h(x)$ is below the x-axis on an interval $(e, f)$, what can be concluded about the behavior of $h(x)$ on that interval?
If the graph of the first derivative $f(x)$ of an integrally-defined function $h(x)$ is increasing on the interval $(g, h)$, what can be said about the behavior of $h(x)$ on that interval?
If the graph of the first derivative $g(x)$ of an integrally-defined function $h(x)$ is decreasing on the interval $(i, j)$, what can be said about the behavior of $h(x)$ on that interval?
Which integral gives the volume of a solid with equlateral triangle cross sections over an interval [a,b]?
Which integral gives the volume of a solid with semicircular cross sections over an interval [a,b]?

study guides for every class

that actually explain what's on your next test

Interval

from class:

AP Calculus AB/BC

Definition

"Interval" also found in:

Subjects (26)

Practice Questions (20+)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

Back

Next

study guides for every class

that actually explain what's on your next test

Interval

from class:

AP Calculus AB/BC

Definition

Related terms

"Interval" also found in:

Subjects (26)

Practice Questions (20+)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

Back

Next