Differentiation of the function would give you an instantaneous rate of change at one point; the tangent line. Repeated differentiation of some functions would give you many such points.
f(x) = X3
= d/dx( X3)
= 3X2
=======graph and see
You can determine if a rate of change is constant, by taking the instantaneous rate of change at multiple points - if they are all equal to each other, it can be assumed that the rate of change is constant. Alternatively, you can differentiate the function (if there is an associated function) - if this comes to a constant i.e. a number, then the rate of change is constant.
Find the derivative
It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.
The derivative is at*ln(a) wheret is the time period, ln is the natural log and a is the multiplier for the annual interest rate: eg if the interest rate is r% then a = (1 + r/100).
Find the slope of the tangent to the graph at the point of interest.
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
Finding the rate of change - in particular, the instantaneous rate of change.
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
Depends. Slope of tangent = instantaneous rate of change. Slope of secant = average rate of change.
This is done with a process of limits. Average rate of change is, for example, (change of y) / (change of x). If you make "change of x" smaller and smaller, in theory (with certain assumptions, a bit too technical to mention here), you get closer and closer to the instant rate of change. In the "limit", when "change of x" approaches zero, you get the true instantaneous rate of change.
The purpose of finding a derivative is to find the instantaneous rate of change. In addition, taking the derivative is used in integration by parts.
Instantaneous velocity is a vector quantity representing the velocity Vi at any point.It is the time rate of change in displacement.
No, velocity is the instantaneous speed of an object, the rate of change would be the acceleration of the object.
The rate of change of position is the velocity. The velocity at a specific point in time is called the instantaneous velocity.
Derivatives are used to find instantaneous rate at which a function changes.