I don't have the Larson book, but I assume it defines the derivative (not _derivation_) of f at x to be the limit of the ratio [f(x+h) - f(x)]/h as h --> 0. Well, you can calculate f(x+h) and you know f(x), so you can see what the ratio is equal to. Then you can see what it becomes closer and closer to as h becomes smaller and smaller.epatjn said:Homework Statement
Here's the question...use the limit defintion to find the derivation of f(x) = x^2-4x
Homework Equations
does this use the defintion of the derivative formula (using Larson, et al 4th edition of Precaclulus graphing with limits...and trying to teach someone what to do, but am at a loss at present on what to do...
The Attempt at a Solution
A limit definition for derivation of f(x) is a mathematical concept that describes the instantaneous rate of change of a function at a specific point. It involves taking the limit of the slope of a secant line as the distance between two points approaches zero.
Understanding limit definition for derivation of f(x) is important because it is the foundation for understanding the concept of derivatives, which are essential in many areas of mathematics and science. It also helps in solving real-world problems involving rates of change.
Sure, for example, if we have the function f(x) = x^2, we can use the limit definition to find the derivative at a specific point, say x = 2. By taking the limit of the slope of the secant line between (2, f(2)) and (2+h, f(2+h)) as h approaches 0, we can find that the derivative of f(x) at x = 2 is 4.
Some common mistakes when using limit definition for derivation of f(x) include not properly understanding the concept, making algebraic errors, and not simplifying the expression before taking the limit. It is important to carefully follow the steps and pay attention to detail when using this definition.
You can start by explaining the concept in simple terms and providing real-world examples. It is also helpful to encourage her to practice solving problems using the limit definition and provide guidance when needed. Additionally, there are many online resources and tutoring services available that can provide further assistance.