You should read this article:nfcfox said:Homework Statement
http://imgur.com/MSkNkno
Homework Equations
The Attempt at a Solution
I know that I would have to take the derivative of H(x) which is G(x)+G'(x)x so then I would need G'(x) which I figured would be f'^-1(x) but I'm not sure about that. Doing that I got a value of 16 which isn't an answer.
The purpose of finding derivatives using a table of values is to approximate the rate of change of a function at a specific point. This can help in analyzing the behavior of the function and making predictions about its future values.
To create a table of values for finding derivatives, you need to choose a range of values for the independent variable (usually denoted by x) and calculate the corresponding values of the function (usually denoted by y). These values are then used to calculate the slope of the secant line between two points and approximate the derivative at a specific point.
Yes, derivatives can be found using a table of values for any type of function. However, the accuracy of the approximation may vary depending on the complexity and smoothness of the function.
The main difference between using a table of values and the limit definition to find derivatives is the level of accuracy. While using a table of values provides an approximation of the derivative, the limit definition gives an exact value. Additionally, the limit definition can be used for any type of function, while a table of values may not provide accurate results for more complex functions.
Yes, higher order derivatives can be found using a table of values. To find the second derivative, you need to calculate the slope of the secant line between two points on the first derivative, and for higher order derivatives, you can repeat this process. However, the accuracy of the approximation may decrease with each successive derivative.