1 Flashcards
What is the concept of a function’s derivative?
The derivative of a function characterizes the rate of change of the function.
What does the derivative of a function at a point x represent?
The limit of the ratio of the function’s increase to the argument’s increase as the argument’s increase approaches zero.
What notation is commonly used to denote the derivative of a function?
f’(x) or dy/dx.
How is the average rate of change of a function defined?
As the ratio of the change in function value to the change in argument over an interval.
What is the formula for the average rate of change of a function f(x) over the interval [x, x + Δx]?
Δf(x) = f(x + Δx) - f(x).
True or False: The average rate of change is constant for all functions.
False.
What is the limit that defines the derivative of a function f(x) at a point x?
lim (Δf(x)/Δx) as Δx approaches 0.
What term describes the process of finding the derivative of a function?
Differentiation.
What historical figures contributed to the terminology of derivatives?
Joseph-Louis Lagrange and Isaac Newton.
The expression f’(x) is read as what?
‘f prime of x’.
What does the notation dy/dx signify?
The derivative of y with respect to x.
Fill in the blank: The derivative is defined as the limit of the _______ as Δx approaches zero.
ratio of the function’s increase to the argument’s increase.
What is the significance of the point where the derivative is calculated?
It indicates the instantaneous rate of change of the function at that specific point.
What does it mean if a function is not linear in relation to its average rate of change?
The average rate of change depends on the interval length.
