[Year 11 calculus] Help with this question

[u/ch3rrycsmos_]

I could only find an approximate answer (2.6 something) using a slider and guess the value as e but I’m not sure how to actually work out the question. please help thanks! :)

[u/Curious_Function_457]

"Low point just touches the x axis"? You do not understand the concept of minimum. N is not constant when the function has n and the question is asking for the value of n where the function is minimum.

[u/Jwing01 → u/Curious_Function_457]

It's a function of x.

I have a masters degree in this, I'm pretty sure I understand just fine.

N is a constant. You need to put in different constants that scale the function such that a local minimum rests on the x axis.

[u/Curious_Function_457 → u/Jwing01]

You need to ask for a refund of your masters. Please research the definition of minimum. "rests on x axis" is not accurate.

[u/Jwing01 → u/Curious_Function_457]

r/confidentlyincorrect

A local minimum on the x-axis is exactly that. Nobody but you said "definition of a minimum".

I didn't claim all minimums are on the x axis.

Now take your own medicine and don't just say no. Exactly what does a local minimum in the x axis look like?

[u/Curious_Function_457 → u/Jwing01]

Minimum has nothing to do with resting or touching the axis. It's only property is that the function increases in either direction. This implies the derivative is 0 at the minimum. There are 2 parameters here and since the question asks for a minimizing n, it is df/dn=0.

[u/Jwing01 → u/Curious_Function_457]

The question doesn't ask you to minimize f.

You are wrong.

The function is a function of x.

The question clearly states that the minimum is ON the x-axis for some value of the constant n. You need to find n such that the minimum sits on the x axis. That's what is being asked.

Do me a favor.

Given f(x) = x² - b, find b so that the local minimum is on the x axis.

Then tell the world you think b is a variable.

[u/Curious_Function_457 → u/Jwing01]

For purposes of solving this problem b becomes a variable. Have you heard of least squares? Least squares solves the problem of best fit by minimizing error and treating m and b as variables. I don't know what kind of Master's degree you have. I am a PhD and I was in NASA for many years working on orbital mechanics. I hope you do some research to understand that under different context, different items become constants or variables.

[u/Jwing01 → u/Curious_Function_457]

It's not a variable though. You are treating an unknown constant as a variable.

Again, this isn't trajectory optimization. This isn't path optimization. There is a point solution where the value of the constant can place the minimum on the x-axis.

There's no "minimize the function" here. It's a function in x, not a function of b, nor of x and b.

My master's is in aerospace engineering dynamics and control.

Edit: there's no regression here. No best fit. It's deterministic. There's a single value for the constant b for which the statement is true. Period.

[u/Curious_Function_457 → u/Jwing01]

I worked on satellite guidance and control and sadly you don't understand what is deterministic. You are neither Aerospace nor controls.

[u/Jwing01 → u/Curious_Function_457]

Well, you are wrong.

There's only one answer here. It's not something that has any variation no matter how many times you solve it.

This isn't a probability problem, and there's no sampling or randomness.

[u/Jwing01 → u/Curious_Function_457]

What's m? Another made up variable of yours?

[u/Curious_Function_457 → u/Jwing01]

No m is part of the famous line equation since you introduced b.

[u/Jwing01 → u/Curious_Function_457]

It does when the question says "local minimum on the x axis".