AP Calculus AB/BC

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Interval

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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).

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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]?

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Interval

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AP Calculus AB/BC

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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.

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