Graphing Equation to a Tangent Line with the TI-89: Raw Transcript

See the original Tangent Line problem done here.

I’m going to graph this for you right now and show you what actually has happened so we’re gonna quit we’re going to goto 3 and we’re gonna quit go back to the home screen we’re going to clear the calculator screen by pushing f1 and 8 which clears the whole screen and were gonna graph we’re gonna put the main…that means the Gold Key here yellow key and F1 so we got the graph points gonna enter gonna graph the original function which is 10 times x divided by X squared x squared plus 1 and we’re going to graph it, that would be the big yellow key and up here it says graph so we’re gonna graph it ok, that’s the function notice the smooth parabolas, if you did this close up which I’ll show you in a second this is all smooth parabolas it’s all calculus can deal with is smooth parabolas now we’re gonna we’re gonna go back and we’re gonna put in the the equation for the tangent line we found so we’re gonna go back to F1 again and we’re gonna put in here we found out that the slope was 5 actually equation was 5, it was 0 times 1 plus 5 so that’s the equation for the tangent line in this. and then we’re gonna graph it again and see what happens you notice that when the slope is 0 you have a horizontal line that’s a big deal in calculus so remember that any time the slope is 0 they always have you make the function equal 0 first derivative and what, and so that means that the line can only touch a graph at one point and so you notice that this is the maximum okay this is the maximum remember that maximum minimums when you graph a function well here it is when your horizontal line touches this graph it only one point and that would be right here now we can take the cursor and you notice this little dot here comes up we can take the cursor we can go up here we can keep going up to x equals of course x equals 0 here’s y equals 4.7
we can go right to five and then we can move it over and we can we can zoom in on that
notice so we can press f2 and then press number 2 here and at that point we’ll press Enter and you notice that you can zoom in at those points pretty neat there’s that point there here’s straight line coming over now this is what we found: okay and you have gotten a 100 percent on this line plus may be understood a little bit better so pretty neat huh? EveryStepCalculus.com go to my programs enjoy my programs pass your calculus class and also subscribe to my blog or future videos to understand or not understand calculus and yet pass your test