Rates of Change

Key Questions

  • Answer:

    As below.


    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.


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


    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.


    Hope this helps.

  • 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!

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  • 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}#


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



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

    I hope that this was helpful.