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Calculus 1 / AB
4 days, 4 hours ago
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The demand function for a product is modeled by p = 400 ? 4x, 0 ? x ? 100, where p is the price per unit (in dollars) and x is the number of units.
In this problem the demand function of the product is modeled by p equals to 400 -4 x. And where access between 02 100. Right So where p. Is the price per unit in dollars? And X. Is the number of units. Okay so first of all from this given um demand function for a product? Right. So we will just right in terms of export will be the value X will be equal to what this will be equals two. 400 minus B upon four. So while I'm doing this I'll let you know afterwards. You will get to know that why I'm doing this. So this is basically you can say that this is the value of X. So now here it is us that determine when the demand is elastic and inelastic. Right? So elastic demand first of all letters straight here A it's his first elastic demand. E. Is given by minus P by X. Into D. X by dp. Right? So this is equation number one. So now you've got to know that why I'm doing this. Okay so this is the basic formula for the elastic demand. Okay so you must remember this now you can find out you can just differentiate this equation what we have found for eggs. So here D exp I. D. P will be equals two Women. Just differentiated, we will be getting one x 4. This is differentiation of 400 will be zero. Right? And differentiation of B will be equal to zero again. Right? So this means that I'm sorry this is differentiation of B will be question -1 here. Right, So this becomes DX by D.P.E. Questo -1 x four. Right, so now we will just put this value. So therefore equation one big guns E equals two -7 by X. Multiplying with -1 x four, which is it be by for X? Right, okay, Now here he will be equals two 400 minus four, X by forward, X. Which is equal to four and 200 minus X divided by four, which is equal to 100 -2. White X. Here. Okay, so this should be not for this should be X. Okay, so he had this cuts off, right to know the demand is elastic. Win. So you can see your dad demand is in a statement He is greater than one. Right? So therefore we can say that 100 -X by X Is greater than one which is equal. There should be X. Who cannot go, there should be X. Here, Okay, So now this becomes a 100 -1. Greater than X. Which is giving us what definitely giving us X is less than 50. Right, You can see that then food. So your interval will be interval will be 0- 50. So you can right here Here, 0- 50. This is the internet. Now we will calculate for in elasticity. So the demand is in elastic then E is less than one. Right? So this means that 100 -X by X. It's less than one Which is giving us 100 is less than two works right? Which is nothing but X is greater than 50. Great. But here you can see that the ranges here given range is strange is between 0 200. Right? So therefore you can say that interventional travel forward demand for being in a last trip. So in the red interval with me what? This will be 50, and this is closed. Okay, so please take care of This interval. So this is 50 open interval and 100 with closed interval because this is also a fitness equals two. Okay, now they live in new always increases are now for the next one B. Part b Okay, one more thing is last year that is determined when demand is of unit elasticity and to your answers as a comma separated list. So here, when e is a quest to one, this is possible when e easy quest to one then 100 minus X by X equals to one which is equals to This will be giving us access, it was 250. Okay, so I answered here will be 50. Right now it is us that use the result of part A to describe the behavior of the venue function. Right, enter your answers as comma separated list. Right, so that the venue always increases till demand Is elastic in 02 50 and Then becomes flat at is X is equal to 50 and then it decreases. Then demand is inelastic. Right? So you can say that. Did he wear new function increases here. You can write give a new function increases, then it is that it X equals to 50 and then decreases. Right? So this is decreases. So this is always solve this problem. I hope this helps. Thank you.
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In mathematics, precalculus is the study of functions (as opposed to calculus, which is the study of change, and algebra, which is the study of operations and their application to solving equations). It is generally considered to be a part of mathematics that prepares students for calculus.
In mathematics, a function (or map) f from a set X to a set Y is a rule which assigns to each element x of X a unique element y of Y, the value of f at x, such that the following conditions are met:
1) For every x in X there is exactly one y in Y, the value of f at x;
2) If x and y are in X, then f(x) = y;
3) If x and y are in X, then f(x) = f(y) implies x = y;
4) For every x in X, there exists a y in Y such that f(x) = y.
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