Final answer:
The correct answer is 1) Derivative. The slope of the tangent line to a curve at any given point is known as the derivative, which represents the rate of change of a function at a specific point.
Step-by-step explanation:
The slope of the tangent line or the slope of the graph is known as the derivative. The correct answer from the provided options is: 1) Derivative. In calculus, the derivative at any point on a curve is the slope of the line tangent to that curve at that point. It visually represents the rate at which the function's value is changing at that specific point.
When considering a function, which is basically an equation that describes a relationship between variables, the derivative indicates how the output of the function (y-value) changes in response to a change in the input (x-value). For instance, if the equation of the line is y = mx + b, where m is the slope and b is the y-intercept, the derivative with respect to x is simply the value of m. This is because, in a linear function, the slope is constant, meaning the rate of change is the same at every point on the line.
In the context of physics, as seen in the reference to velocity, if you have an X vs. t graph, where 'X' stands for position and 't' is time, the slope of the curve at any given point gives you the instantaneous velocity. Mathematically, calculating this slope involves taking the derivative of the position with respect to time.