implicit differentiation follow up question

[silver forge]

I differentiated to get

which is correct part i

however part ii

you have to set to zero

im just confused how you'd then solve for x or y,

[lament slate]

4-2x = 0

[silver forge]

can you just explain why

please

ohhhh

because the stationary point is where the y axis doesn't change

so y = 0

right?

[lament slate]

No

You just solve (4-2x)/4y = 0 by multiplying both sides by 4y

[modern zephyr]

x=2

then find d^2y/dx^2

substitute in x=2

then if its bigger than 0 , its a minimum and if it's smaller than 0, it's a maximum point

local min and max

[lament slate]

‘You do not need to determine their nature’

[silver forge]

4 - 2x = 4y, would then assume y = 0, as it’s a stationary point??

[lament slate]

…..

What’s 4y multiplied by 0

[silver forge]

OHHHH 💀💀💀💀💀