Geogebra

[lost wyvern]

I have to find highest point in the z-axis on a 2-variable function.
How do I do this?

[hidden lynx]

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[lost wyvern]

@pseudo hatch

[pseudo hatch]

oh um yeah that idek lmao

I was hoping it was very basic advice

sorry

[lost wyvern]

alright

[pseudo hatch]

just wait someone will help

[lost wyvern]

ye

looks like that

thats the function

[mortal moss]

No need to use nested ifs.
f(x, y) = (a/b) if(x > 0 ∧ y > 0 ∧ x + y < 40, (1 + x/100)/(1 - y/100))
Apart from that, the usual approach works. Though, here it will work only if you specifically include the boundary by doing f(x, y) = (a/b) if(x >= 0 ∧ y >= 0 ∧ x + y <= 40, (1 + x/100)/(1 - y/100)).

1. Find critical points in the interior, if there are any.
2. Find critical points on the boundary. If it's given piecewise, also consider the boundary points between the pieces.
3. Compare the values at all the critical points you've found.

[lost wyvern]

how do i find critical points on the boundary?

[mortal moss]

Parametrize it. Here it's pretty easy, considering it's piecewise linear.

[lost wyvern]

i dont know what parametrize or piece means

[mortal moss]

You should review parametric and piecewise functions, then.

[lost wyvern]

ok, do you want to get pinged if i need help again?

[mortal moss]

Well, I check help posts here relatively frequently if I'm not busy. You can just reply to my comment, no need to specifically ping me.

[lost wyvern]

ok

thanks

[lost wyvern]

btw, there are no parametrics. i used the wrong function at the start. the function without parametrics is below. will this change the problem?

[mortal moss]

What do you mean by "no parametrics"?

[lost wyvern]

like no a or b, just constants

[mortal moss]

Well, that doesn't matter.

But that's not what I meant above.

The boundary of your region is described by three inequalities: x ≥ 0, y ≥ 0, x + y ≤ 40. So, we can divide it into three pieces and parametrize them as follows:

1. x = 0, y = t, 0 ≤ t ≤ 40
2. x = t, y = 40 - t, 0 ≤ t ≤ 40
3. x = t, y = 0, 0 ≤ t ≤ 40
   Note that t is unique for each case. If that confuses you, you can call the parameters by different names, like t1, t2 and t3.

[lost wyvern]

what is t

[mortal moss]

Parameter.

[lost wyvern]

i believe the highest point is on the boundary, could you help me find it?

[mortal moss]

Try it yourself first.

As I said above, check each piece of the boundary, then the points between the pieces.

[lost wyvern]

wdym by piece, i didnt study math in english

[mortal moss]

I don't really know how to explain it in another way. And neither did I.

[lost wyvern]

i found out what i wanted to find out