All Questions
Tagged with applications functions
30
questions
0
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1
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63
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Maximum and Minimum of a cubic function
Maximum value of function
$y = x^3-5x^2+2$
a) 5
b) $\infty$
c) 2
d) -5
We know to find maximum value of a function we take first derivative of the function and make it zero and get some point. And ...
- 195
4
votes
6
answers
682
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Is $x^3$ really an increasing function for all intervals?
I had an argument with my maths teacher today...
He says, along with another classmate of mine that $x^3$ is increasing for all intervals. I argue that it isn't.
If we look at conditions for ...
- 45
3
votes
1
answer
134
views
A "perfect" (chess) rating system
Assume we want to have a player rating system with the following conditions:
For simplicity, no draws.
If A wins against B with ratings $a,b$, their new ratings are $a'=f(a,b),b'=g(a,b)$.
Most ...
- 745
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0
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40
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Proving a function decays polynomially
Let $f:\mathbb{R}\to\mathbb{R}$ be such that $f(x)=O\left(\left(\frac{1}{\log x}\right)^{\lambda}\right)$ as $x\to\infty$ for some constant $\lambda\in\mathbb{R}$. Can we prove that $f$ decays ...
user1022331
0
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0
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60
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Representing Submodular Functions As Maxima of Additive Functions
According to this paper, "every submodular function can be represented as a maximum of additive valuations." It gives an algebraic description as well, but I am having trouble internalizing ...
- 1,912
1
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0
answers
72
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How units didn't change while differentiation?
In this example, rate of change has units cm², while the original quantity, area, also has same units. I learnt that units change just like normal ratio, that is dA/dr will have same units as A/r, so ...
- 61
3
votes
2
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126
views
How are the functions determined for real-world applications (business, population models, etc.) of calculus?
The following problem has been taken from Paul's Online Notes:
"We need to enclose a rectangular field with a fence. We have 500 feet of fencing material and a building is on one side of the ...
- 33
3
votes
1
answer
67
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Seemingly conflicting notions of a function
Throughout my mathematical education, I have seen a few, seemingly, different and conflicting notions of what a function is:
A function is a a type of mathematical object that maps every element of a ...
user997478
0
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0
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48
views
Find a function
It's a cuttout from Rempe article "A mathematical model of the sleep/wake cycle" about a function which I don't understand how to describe: $h(t)$ decays exponentially while the system is asleep
and ...
- 480
1
vote
1
answer
48
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Purpose of rotation of a Function or Graph
You are able to rotate any function by an arbitrary angle around the origin using the formula,
$$y\cos\theta-x\sin\theta=f(x\cos\theta+y\sin\theta)$$You can also do similar rotations for polar graphs, ...
- 388
0
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1
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81
views
Closed-form solution for $f(x)/x=y$ using $f^{-1}$
I'm programming a piece of math that requires solving an equation of a form $f(x)/x=y$. Now I already have $f^{-1}(z)$ coded (efficiently, and not by me) so I'd prefer using this implementation ...
- 3,202
0
votes
2
answers
314
views
Determine if function is injective, surjective, bijective [closed]
For
$$f : \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z}$$
$$f(m,n) = 3m + 2n -1$$
I think it's injective, but don't know how to prove it. I've been trying numbers for m and n.
user481368
9
votes
4
answers
459
views
"Class" of functions whose inverse, where defined, is the same "class"
Please excuse the amateurish use of the term "class", I don't know what the exact term is for what I'm looking for.
Anyway, details.
I'm asking specifically about real-valued functions on the real ...
- 101
1
vote
1
answer
52
views
Unit decomposition by three continuous functions
My current research project involves adaptive weights for three different loss functions so that I hope each the objective can focus on the different size of objects when given a different size of the ...
- 255
0
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1
answer
32
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The shortest route of an amphibian vehicle
Let be the x axis the coast.
The speed of an amphibian vehicle in the upper half-plane (land) is $v_{1}$ and in the under half-plane (sea) is $v_{2}$ and $v_{2}<v_{1}$.
From the starting point (1,...
- 2,022