The area under a function's curve is equal to the value of its antiderivative, calculated with the same bounds.

A function is increasing where its first derivative is positive.

A function is decreasing where its first derivative is negative.

Relative extrema occur where the first derivative is zero or undefined and changes sign.

A function is concave up where its second derivative is positive and concave down where it is negative.

Inflection points occur where the second derivative changes sign.

Area below the x-axis is considered negative when calculating definite integrals.

When $f'(x) > 0$, $f(x)$ is increasing. When $f'(x) < 0$, $f(x)$ is decreasing.

The slope of $f'(x)$ indicates the concavity of $f(x)$. Positive slope means concave up, negative slope means concave down.

Evaluate the function at critical points and endpoints; the smallest/largest value is the absolute minimum/maximum.

Critical Point: $f'(x) = 0$ or undefined, potential for max/min. | Point of Inflection: $f''(x)$ changes sign, change in concavity.

Relative Extrema: Local max/min within an interval. | Absolute Extrema: Overall max/min over the entire domain.

Increasing: $f'(x) > 0$, function is rising. | Concave Up: $f''(x) > 0$, function curves upwards.

Decreasing: $f'(x) < 0$, function is falling. | Concave Down: $f''(x) < 0$, function curves downwards.

Function: Represents the value of the function at each point. | Derivative: Represents the rate of change of the function at each point.

Definite Integral: Computes the area under a curve between two limits, resulting in a numerical value. | Indefinite Integral: Finds the antiderivative of a function, resulting in a family of functions.

$f'(x)$: The derivative of $f(x)$, representing the instantaneous rate of change. | $\int f(x) dx$: The antiderivative of $f(x)$, representing the accumulation of $f(x)$.

First Derivative Test: Examines the sign change of $f'(x)$ around a critical point. | Second Derivative Test: Uses the sign of $f''(x)$ at a critical point to determine concavity and thus whether it is a max or min.

Local Extremum: A maximum or minimum within the interior of an interval. | Endpoint Extremum: A maximum or minimum that occurs at the boundary of an interval.

Average Rate of Change: The slope of the secant line between two points. | Instantaneous Rate of Change: The slope of the tangent line at a single point, given by the derivative.

A function that represents the accumulated area under a curve from a fixed point to a variable point.

A function whose derivative is the given function.

The theorem that links the concept of the integral of a function with the concept of the derivative of a function.

A point on a curve where the concavity changes.

A point where the function's value is greater than or equal to the values at all nearby points.

A point where the function's value is less than or equal to the values at all nearby points.

A curve that opens upwards.

A curve that opens downwards.

The integral of a function between two points, representing the accumulation of the function's values.

A point where the derivative of a function is either zero or undefined.