What is a derivative of a function in calculus?
What is a derivative of a function in calculus?
A derivative is a function which measures the slope. It depends upon x in some way, and is found by differentiating a function of the form y = f (x). When x is substituted into the derivative, the result is the slope of the original function y = f (x).
What does f2 mean?
Q: What does f'(2) mean? A: f'(2) stands for the value or expression for the first derivative of the function, f with respect to an independent variable, say x, at x = 2. For example, consider the function f(x) = 3x²
Is it possible to find the derivative at every point?
It seems reasonable to conclude that knowing the derivative of the function at every point would produce valuable information about the behavior of the function. However, the process of finding the derivative at even a handful of values using the techniques of the preceding section would quickly become quite tedious.
What is the derivative of a function?
The derivative function, denoted by , is the function whose domain consists of those values of such that the following limit exists: . exists. More generally, a function is said to be differentiable on if it is differentiable at every point in an open set , and a differentiable function is one in which exists on its domain.
What is the derivative of the function with a horizontal tangent?
The derivative is zero where the function has a horizontal tangent. Use the following graph of to sketch a graph of . The solution is shown in the following graph. Observe that is increasing and on . Also, is decreasing and on and on . Also note that has horizontal tangents at -2 and 3, and and .
Is the derivative of the function increasing or decreasing over time?
Both functions are increasing over the interval At each point the derivative Both functions are decreasing over the interval At each point the derivative
