Certain functions, when solving to find the zeros (value which makes the function equal zero), the only value which will work has an imaginary component. Note that a parabola (graph of a quadratic or 2nd order polynomial) can touch the x-axis at a single point, or 2 points or no points. If it does not touch or cross the x-axis, then the root (or zeros) of the function are complex with imaginary components.Technically, all real numbers are a subset of complex numbers, so all numbers are complex - but this is not how we normally refer to them. We usually say that a number is real, or it is imaginary, or it is complex.
Set the first derivative of the function equal to zero, and solve for the variable.
The "critical points" of a function are the points at which the derivative equals zero or the derivative is undefined. To find the critical points, you first find the derivative of the function. You then set that derivative equal to zero. Any values at which the derivative equals zero are "critical points". You then determine if the derivative is ever undefined at a point (for example, because the denominator of a fraction is equal to zero at that point). Any such points are also called "critical points". In essence, the critical points are the relative minima or maxima of a function (where the graph of the function reverses direction) and can be easily determined by visually examining the graph.
The domain of a rational function is the whole of the real numbers except those points where the denominator of the rational function, simplified if possible, is zero.
You find the average rate of change of the function. That gives you the derivative on different points of the graph.
The fixed points of a function f(x) are the points where f(x)= x.
Certain functions, when solving to find the zeros (value which makes the function equal zero), the only value which will work has an imaginary component. Note that a parabola (graph of a quadratic or 2nd order polynomial) can touch the x-axis at a single point, or 2 points or no points. If it does not touch or cross the x-axis, then the root (or zeros) of the function are complex with imaginary components.Technically, all real numbers are a subset of complex numbers, so all numbers are complex - but this is not how we normally refer to them. We usually say that a number is real, or it is imaginary, or it is complex.
No. If you have more than two points for a linear function any two points can be used to find the slope.
Take the derivative of the function and set it equal to zero. The solution(s) are your critical points.
Set the first derivative of the function equal to zero, and solve for the variable.
To determine the maximum displacement, you need to calculate the peak value of the displacement function. This is done by finding the extreme values (maximum or minimum) of the function, typically by taking the derivative and setting it to zero to find critical points. Once you have these critical points, evaluate the function at those points to find the maximum displacement.
The "critical points" of a function are the points at which the derivative equals zero or the derivative is undefined. To find the critical points, you first find the derivative of the function. You then set that derivative equal to zero. Any values at which the derivative equals zero are "critical points". You then determine if the derivative is ever undefined at a point (for example, because the denominator of a fraction is equal to zero at that point). Any such points are also called "critical points". In essence, the critical points are the relative minima or maxima of a function (where the graph of the function reverses direction) and can be easily determined by visually examining the graph.
The domain of a rational function is the whole of the real numbers except those points where the denominator of the rational function, simplified if possible, is zero.
There are many different online sources where one could find free web analytic software. Some of these sites include Piwik, GoStats, Gomez, and WebStats.
Google provides a powerful image search function that one could use to find pictures of intricate machines.
You find the average rate of change of the function. That gives you the derivative on different points of the graph.
The structured technique of Analytic Hierarchy Process has a lot of information which can be gathered from Wikipedia and also online from the AHP official website.