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Good day students welcome to mathgotserved.com in this clip were going to be going over how to calculate the average rate of change also known as the slope of the secant line don't forget to visit our email@example.com for access to a wide variety of math tutorials ranging from algebra on the way to calculus let's take a look at the instructions for the examples were going to be going were to find the average rate of change in the the equation of the secant line with that you're on the given input files before we get started let's take a look at the formula that will be guiding our problem-solving process okay the average rate of change of: Iraq on it is about 80 this is also known as the slope of the secant line is given by F of the minus F of a divided by -8 to this formula is the same thing as why two minus why one over X2 minus X one of the remember what formula this is this is the formula for the slope of the line given two points rise over run so this formula that we looking at here is just and advanced notation version of the formula you ready learn in one okay so FOB minus F of a is simply arise and the minus a is your okay so with that in mind is go ahead and take a look at our first example number one we have the function F of X equals negative 2X square minus X plus one on the interval I'll zero, one okay so in other two find the average rate of change we need for ingredients we need FOB minus F of a over B -8 so need FOB F of a be in a right so you want to note that this is the interval I'll 01 is an is have all not important okay so is an integral along the x-axis of this first the lower bound is a and the upper bound is the a is equal to zero next thing we need to find is F of a a of F of zero which simply means we have to evaluate this function at X equals zero okay so you have negative to times zero square -0+ one evaluating the end up with positive one next thing we need is on coming be the is one and then we need to find F of be sin B is one F of be is equal to F of one so FOB that we means we evaluate this function at X equals one let's go ahead and do that so we going to have -2 times one is where minus one plus one okay let's will of the nation entry it correctly it you always this function you going to end up with negative to these two counsel out out of to zero now we have all the ingredients we need to calculate hour average rate of change so our average rate of change on the interval I'll one, to actually zero, one on the interval I'll zero, one is simply F of one minus F of zero divided by one -0 okay so we use a result became up with here F of one is negative to minus F of zero which is one divided by one -0 right and then went up with -3 over one which equals -3 so there goes our average rate of change were also asked to calculate the all equation of the secant line to this curve on this interval out so how do you find the equation of the line square and write down the formula for the be part equation of the line of let's use the formula why minus why one equals and X minus X one okay so we defeated point and home the slope okay so our a is simply X one which is zero our be is why one which is what is why one why one is F of zero is always a function at zero which is going to be let's see what F of zero is F of zero again one right to that goes our points in our slope and is the average rate of change evaluated at 01 which we did earlier and that's -3 okay so weekly have the two points we need we can okay pick out X one why one X one why one is the same thing as a, F of a using and advanced notation or we can use X to Y to which is the, F of be write it doesn't matter which point you think as a list of point is of the line that equation to be accurate sorry so we have everything we need to write down the equation of our secant line so equation of our secant line the why minus why one which is one equals -3 times X minus X one which is zero okay so this is the answer in points with one if you wanted to write this in slope intercept form we just simply get why myself so all you do is you have why I will to both sides a have negative 3X plus one people are the same thing we just in different forms right okay now let's go ahead and show you shortcut on how to find the slope of the secant line on a given interval using the TI 89 titanium calculator okay so let's go ahead and try out there were going to do first is way to the sine function a call it negative to X square minus X plus one so how do we define a function all you simply do is store the function negative to X square minus minus X plus one of the simplest stories in F of X is targeting out file Anbar here is F parenthesis X okay to just type in the function in story in F of X enter a calculator to be done when there are does that mean is means that this expression has in store in F of
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