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Current time:0:00Total duration:3:56

Matching functions & their derivatives graphically (old)

Video transcript

the function f of X is shown in green the sliding purple window may contain a section of an anti derivative of the function f of X so essentially it's saying this green function is potentially the derivative of or part of this green function is potentially the derivative of this purple function and what we need to do is it says where does the function of the sliding window correspond to the anti derivative of our function the anti derivative of f of X usually right as big f of X this is just saying that f of X is the derivative of or lowercase F of X is just the derivative of big f of X so at what point at what point could the derivative of the purple function and I'm going to move the purple function around where could it be where can the derivative of that be the green stuff so just let's just focus on the purple stuff first so the derivative we can just view it as the slope of the tangent line between this point and this point we see that we have a constant negative slope and then we have a constant positive slope so let's see where where here do we have a constant negative slope well now here the slope is zero and it gets more negative here we have a constant positive slope not a constant negative slope here we have a constant negative slope so maybe it matches up over there so here here we have a constant negative slope but then we don't have a pot on the purple function we have a positive slope but where they where the potential derivative is here we just have a slope of zero so this doesn't match up either so it looks like in this case there's actually no solution let's see if this works out yes correct next question let's do another one a function f of X is shown in purple the sliding green window may contain a section of its derivative so now we're trying to say at what point of this purple function might the derivative look like this green function so in this green function if this is the functions derivative here the slope is very negative it goes to zero and then the slope gets positive so let's think about it so over here the slope the slope is just a constant negative so that won't work if we shift it over here our slope is very steep in the negative erection and then it gets less and less deep in the negative direction and it goes all the way and then over here the slope is zero and over here if this is a derivative it seems to match up the slope is zero and then it gets more and more steep in the positive direction so this matches up it looks like over this interval the green function is indeed the derivative of this purple function so let's see let's check our answer correct next question let's do another one this is exciting a function f of X is shown in green the sliding purple window may contain a section of an anti derivative of the function f of X so now we say let's try to match up this let's match up this little purple section to its derivative so the green is the derivative of the purple function is the thing we're taking the derivative of so if we just look at the purple we see that we have a neg a constant negative slope in the first part of it then our slope so let me just look for where I can find a constant negative slope so here this is a constant positive slope this is not a constant slope this is constant positive okay here a constant negative slope let's see if this works so over this interval between here and here my slope is a constant negative and indeed it looks like a constant negative and you see it's a constant negative one and over here you see the derivative is right at negative one and it's constant so that part looks good and then when I look at the purple function my slope is zero starting off then it gets more and more steep in the negative direction and so my slope is zero and it gets more and more negative so this indeed seems to match up so let's check let's check our answer yes got it right I can keep doing this this is so much fun