Rates of Change

Key Questions

  • How does rate of change relate to slope?

    Answer:

    As below.

    Explanation:

    Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line.
    The vertical change between two points is called the rise, and the horizontal change is called the run.
    The slope equals the rise divided by the run: .
    This simple equation is called the slope formula.

    https://www.slideshare.net/jessicagarcia62/rate-of-change-and-slope-42193195

    If y = f(x+h) = 3 (x + h)^ 2, (Just plug x + h in for x). So, you get this:

    https://www.youtube.com/watch?v=xBdo-D1RiNs

    The instantaneous rate of change, or derivative, can be written as dy/dx, and it is a function that tells you the instantaneous rate of change at any point.

    y' = f'(x+h) = (d/(dx)) (3*(x)^2) = 6x * 1 = 6x

    . For example, if x = 1, then the instantaneous rate of change is 6.

    Rate of Change Formula helps us to calculate the slope of a line if the coordinates of the points on the line are given. ... If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates.

    http://www.studygeek.org/calculus/rate-of-change/

    Hope this helps.

    sankarankalyanam · 1 · Apr 15 2018
  • What is rates of change?

    Rate of change is a number that tells you how a quantity changes in relation to another.
    Velocity is one of such things. It tells you how distance changes with time.
    For example: 23 km/h tells you that you move of 23 km each hour.

    Another example is the rate of change in a linear function.

    Consider the linear function: y=4x+7
    the number 4 in front of x is the number that represent the rate of change. It tells you that every time x increases of 1, the corresponding value of y increases of 4.
    If you get a negative number it means that the y value is decreasing.
    If the number is zero it means that you do not have change, i.e you have a constant!

    Examples:
    enter image source here

    Gió · 1 · Dec 21 2014
  • How do you calculate rate of change?

    Average Rate of Change

    The average rate of change of a function f(x) on an interval [a,b] can be found by

    ("Average Rate of Change")={f(b)-f(a)}/{b-a}

    Example

    Find the average rate of change of f(x)=x^2+3x on [1,3].

    f(3)=(3)^2+3(3)=18

    f(1)=(1)^2+3(1)=4

    ("Average Rate of Change")={f(3)-f(1)}/{3-1}={18-4}/{2}=14/2=7

    I hope that this was helpful.

    Wataru · 2 · Nov 13 2014

Questions

Graphs of Linear Equations and Functions