Hello everybody this is Tom from everystepcalculuseverystepphysic.com. We are going to do a maximum and minimum problem in graphing functions index eight to get to my menu we’re going to scroll down here to local max and min there is it there you can do all these things after you put the function in I always tell you to start on graph paper because when you have a test you are supposed to find these things through derivatives etc. then graph it by hand on a peace of paper, so you find the points and continue to graph it so we are going to enter the functions we have to press alpha before you enter anything in these entry lines here, alpha function 6*x^3-9*x^2+8 it’s going to show you what you have entered and you can change it if you want, say it’s okay and then we are going to scroll down here to local max and min and we are going to wait for it to load, this is busy when it’s loading the program, it only does that when your doing it for the first time you load it and the rest of the time it is very quick and first we find the first derivative and then we say it is equal to zero and factor it and then find the x values x= 0 or x=1 theses are critical numbers alone the x-axis they are not critical points, critical point is when you put theses into toe original functions then solve for y and you get the y value and that’s a point and we’ve done that here and (x,y) = (0,8), (x,y) = (1,5) these are the points, very important and a lot of professors don’t make that clear and then to find whether it’s a max or min you put the critical numbers into the second derivatives and if the answer is negative then you know you have a maximum and if the answer is a positive then it’s minimum, you notice that they are opposite positive minimum, negative maximum, so we find the second derivative here it is here put x=0 in for that we get -18, -18 means it’s a maximum now notice this is a positive and therefore it is a minimum, now I graph this for you so you can see exactly what is happening and you can see here at 0,8 we have a maximum at 1,5 we have a minimum. Pretty neat huh, everystepcalculus.com go on my site buy my programs pass calculus, have a good one bye bye.

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