| Term | Definition |
|---|---|
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| independent variable | The input variable of a function, typically represented as x, with respect to which the rate of change is measured. |
| instantaneous rate of change | The rate at which a function is changing at a specific point, represented by the derivative at that point. |
| Term | Definition |
|---|---|
| acceleration | The derivative of the velocity function with respect to time, representing the rate of change of velocity for a moving particle. |
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| position | The location of an object along a straight line, typically represented as a function of time. |
| rate of change | The measure of how quickly a quantity changes with respect to another variable, often time. |
| rectilinear motion | Motion of a particle along a straight line, characterized by changes in position, velocity, and acceleration. |
| speed | The magnitude of the velocity vector, representing the rate at which a particle is moving without regard to direction. |
| velocity | The derivative of a position function with respect to time, representing the rate and direction of change of position for a moving particle. |
| Term | Definition |
|---|---|
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| rate of change | The measure of how quickly a quantity changes with respect to another variable, often time. |
| Term | Definition |
|---|---|
| chain rule | A differentiation rule that provides a method for finding the derivative of a composite function by multiplying the derivative of the outer function by the derivative of the inner function. |
| product rule | A differentiation rule that states the derivative of a product of two functions equals the first function times the derivative of the second plus the second function times the derivative of the first. |
| quotient rule | A differentiation rule used to find the derivative of a quotient of two differentiable functions. |
| related rates | Problems in which the rates of change of two or more related quantities are connected, and the derivative is used to find an unknown rate of change from known rates. |
| Term | Definition |
|---|---|
| derivative | The instantaneous rate of change of a function at a specific point, representing the slope of the tangent line to the function at that point. |
| rate of change | The measure of how quickly a quantity changes with respect to another variable, often time. |
| related rates | Problems in which the rates of change of two or more related quantities are connected, and the derivative is used to find an unknown rate of change from known rates. |
| Term | Definition |
|---|---|
| locally linear approximation | An approximation of a function's behavior in a small region around a point using a linear function, typically the tangent line at that point. |
| overestimate | An approximation that is greater than the actual value of a function. |
| point of tangency | The point where a tangent line touches a curve. |
| tangent line | A line that touches a curve at a single point and has a slope equal to the derivative of the function at that point. |
| underestimate | An approximation that is less than the actual value of a function. |
| Term | Definition |
|---|---|
| indeterminate forms | Limit expressions that do not have a determinate value without further analysis, such as 0/0 or ∞/∞. |
| L'Hospital's Rule | A method for evaluating limits of indeterminate forms by taking the derivative of the numerator and denominator separately. |