a tricky question in calculus

>>8714570
You have written out that shitter of a question, it was not asked in your uni course.

Come clean anon, just by looking at that I would be highly surprised if it had solutions.

>>8714570
nice try dude. take your homework somewhere else

>>8714570
bait
or you go to a very shitty uni

>>8714570
The only part of R where it works is {1} and it gives 0. You found your maximum AND minimum.
Are you literally retarded?

>>8714570
f(x)=0 everywhere it is defined (i.e. on {-1, 1})

>>8714570 (OP) it was asked few years ago, I'm now in a phD

>>8714570 (OP)
lmao i know how to use the chain rule and those shits

>>8714570 (OP)
try to enter the function in wolframalpha and youll realize the function is not what you expected

>>8714593
it is defined on -1 too
Are you literally retarded ?

>>8714570 (OP) >>8714570 (OP)

youre right, all students made the derivative with the rule chain whitout thinking, and almost all found a non existent local maximum at 0

you cannot define a derivative in the discrete space {-1,1} since you need at least a limit point to define a limit kek

>>8714570
One part of the function is only defined in [-1,1]
The other part of the function is defined only in [-inf,-1] union [1,inf]

So this function is only defined at {1,-1}

Now, a point x is a global maximum if and only if for every x element of the domain, f(x) is less than or equal than f(c)

So now lets check it for 1

f(1) = 0
and f(-1) = 0
and 0 is less than or equal to 0

so 1 is a maximum. The same reasoning shows that -1 is a maximum. And the same reasoning shows that 1 and -1 are also minima.

>>8714583
>>8714587
>>8714589

If you think about it, this is a good question to get the little calc I babby retards to try to think for the first time in their life about what a definition fucking says, instead of plugging and chugging with formulas and dick jerking.

>>8714605
You literally go to a community college if nobody in your class realized they were differentiating a function that's not even defined

>>8714610
the definition of the function is wrong, though.
it says the domain is R when, for example,
0 is in R but f(0) is not real.

>>8714612
its defined in a discrete space of two points {-1,1}, but the derivative not, and the question never say nothing about derivatives

>>8714613
>it says the domain is R when, for example,
>0 is in R but f(0) is not real.

I remember back in high school we sayd functions were defined in the real numbers, when really they were defined in a subset of the real numbers.

Just some dumb notation, probably to give the kids the hint that if they start taking complex derivatives, they have gone way off.

>>8714583
>>8714613
This is what I was getting at. It is not a function with real solutions, even though it is presented as such.

>>8714614
>f -> R
>only in 2 discrete points

Seems like a real function alright.

>>8714618
>Seems like a real function alright.

You can always think of a "real" function which is not defined somewhere to be a function such that it maps those points to the empty set.

>>8714617
You trying to tell me your notation is justified because it's okay to have an unreal solution midway through your function?
Of the 3 domain integers your function includes, 30% of them give an non-real range.

>>8714617
>>8714618

the issue is, when you consider the formal definition of a function as a set of ordered pairs satisfying, among other properties, (a,f(a)) is in f for all a in Domain, the function is clearly ill-defined.

this question made me consider the case of cardano formula where there is a complex "intermediate" for a certain evaluation of a function, but both the input and the output are real. would that function be well defined?

>>8714631
I would imagine that as the complex intermediate does not interfere with the actual mapping of each domain to a real range, it is still a well defined function.
It is only when a input ceases to give a real output (OP's case) when it gets fucky.

>>8714610
>If you think about it, this is a good question to get the little calc I babby retards to try to think for the first time in their life about what a definition fucking says, instead of plugging and chugging with formulas and dick jerking.
yup, it's a perfect homework question

might net you a few math majors too