So we're given this information here that if we sell a DVD player how we sell 12 units and then if we sell it for 200 we sell 500 units. So we're going to, um, find a function of the demand as, ah, very boat or a function of the demand as a function of the price. Okay, so the demand here is the 12 or is how many units sold? So this is the demand, and we're going to call that, uh, variable d and then this is gonna be our price. But I'm gonna call variable p. So are the slope for our demand is going to be the change in demand in demand. Um, divided by the change in price. So are changing a man it's going to be equal to. So, for example, if we go from ah 15 or from 12 to 15 are change is going to be 15 minus 12 divided by and then ah, we went from 2 50 to 200 which means that we go 200 minus 250. So our slope then for our function, is when a vehicle to negative and then we have or sorry, three divided by negative 50. So this is the slope of our demand function. Now we need to plug it into a slope point slope form. So we're gonna have demand, uh, demand minus. Let's say some initial demand with Swiss say 12 or let's do 15 do U minus 15 and then this is gonna be good to our slope. So three or negative, 3/50 times. Let's say our initial price WAAS. So our price with the 15 units is 200. So we'll do p um minus 200. So then now we're gonna have that demand. It's gonna be equal to so negative 3/50 times p. And then this times this it's going to be able to will have plus, so 600 divided by 50 that's gonna be able to 12 and then we're gonna move this over here as well. So then it becomes plus 15. So our demand function is going to be negative. 3/50 p and then plus 27. So now we need to find the range of our, um, well, our domain. So if you notice here, um, if we increase in price for going to decrease in demand. So increase in price means a decrease in demand are an Until eventually that will get our demand is going to be equal to zero. So if we have a demand of zero, then our demand so negative 3/50 p plus 27 in order to reach a demand of zero than our price, it's gonna have to be will solve four p. So negative 27 is equal to negative 3/50 p, then times 50/3. So negative, 27 times negative, 50/3. So first we can divide 27 by three. So that's gonna become nine. The also the plus will cancel out. So we have nine times 50. So then we're going to get a price of 450. So when are prices 450? Our demand will be zero. Also, our price cannot be negative, right? So our price has to be some positive number. So our price it's going to be in the range of zero, not including zero, since we have to charge something off until our maximum price is going to be 450 because at that price. Our demand will be zero any higher than that. And then, um who won't have anything or our demand will be negative, which can't happen.