There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
How many units should be rented out in order to optimize the monthly rental profit?
What is the maximum monthly profit realizable?
Given profit function ,
To maximize profit
as per second derirative test profit is maximum at
Also , maximum profit
To maximize the montly rental profit, 89 units should be rented out, 54052$ be the maximum monthly profit
In a regression analysis, the variable that is being predicted is the "dependent variable."
a. Intervening variable
b. Dependent variable
d. Independent variable
What is in math?
Repeated addition is called ?
Multiplicative inverse of 1/7 is _?
Does the series converge or diverge this
Use Lagrange multipliers to find the point on a surface that is closest to a plane.
Find the point on closest to using Lagrange multipliers.
I recognize as my constraint but am unable to recognize the distance squared I am trying to minimize in terms of 3 variables. May someone help please.
Just find the curve of intersection between and
Which equation illustrates the identity property of multiplication? A B C D
The significance of partial derivative notation
If some function like depends on just one variable like , we denote its derivative with respect to the variable by:
Now if the function happens to depend on variables we denote its derivative with respect to the th variable by:
Now my question is what is the significance of this notation? I mean what will be wrong if we show "Partial derivative" of with respect to like this? :
Does the symbol have a significant meaning?
The function is a differentiable function at such that and for every . Define , with the given about. Is it possible to calculate or , or ?
Given topological spaces , consider a multivariable function such that for any , the functions in the family are all continuous. Must itself be continuous?
Let be an independent variable. Does the differential dx depend on ?(from the definition of differential for variables & multivariable functions)
Let and let . Then find derivative of , denoted by .
So, Derivative of if exists, will satisfy .
if and ,
1) 𝑎𝑛𝑑 so his means that the function is a function of one variable which is
2) while we were computing 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒𝑠 we treated and as two independent variables although that changes as changes but while doing the 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒𝑠 w.r.t we treated and as two independent varaibles and considered as a constant
Let be defined as
then check whether its differentiable and also whether its partial derivatives ie are continuous at . I dont know how to check the differentiability of a multivariable function as I am just beginning to learn it. For continuity of partial derivative I just checked for as function is symmetric in and . So turns out to be
which is definitely not as . Same can be stated for . But how to proceed with the first part?