Question

Hey! for 9x^2+y^2-90x+2y+190,where does the derivative =0 and where is it undefined?

Answer 1

The derivative is not zero since this is not a constant

Answer 2

oops i wasnt paying attention as usual

Answer 3

you want
\[\frac{dy}{dx}\] yes?

Answer 4

ready? here we go

Answer 5

\[18x+2yy'-90+2y'=0\]

Answer 6

i assume this beast is set = 0, otherwise it does not define a curve, and therefor no implicit function. yes?

Answer 7

well,its supposed to be a conic equation

Answer 8

well if it is an "equation" it must be equal something right?

Answer 9

yeah..it was =to 0

Answer 10

\[ 9x^2+y^2-90x+2y+190\]as it is is simply an expression.

Answer 11

how did i guess?

Answer 12

ok now we solve for y' using elementary algebra

Answer 13

n its -18x+19/2y+2 right

Answer 14

i dont get where it wud b undefined?

Answer 15

supposing it's dy/dx...
becomes 0 when x=5

Answer 16

\[18x+2yy′−90+2y′=0\]
\[(2y+2)y'=90-18x\]
\[y'=\frac{90-18x}{2y+2}=\frac{45-x}{y+1}\]

Answer 17

did i make an algebra mistake, because that is what i got

Answer 18

anyway it is undefined if y = 1

Answer 19

ohh no u didnt..minz was wrong

Answer 20

ok then i was just wrong too. it is undefined if y = -1

Answer 21

ohh..so to find undefined values..make the deniminator = to 0?

Answer 22

xactly

Answer 23

i know back to the dungeon for me...

Answer 24

thnk u soo much!

Answer 25

welcome. btw 0 if x = 45

Answer 26

9x^2 +y^2 -90x +2y +190

18x +2y.y' -90 +2.y'

y'(2y +2) = -18x +90

\[y' = \frac{-9x +45}{y+1}\] is what I get :)

Answer 27

ya its undefined when x=-1

Answer 28

ohhok..thnk u all so much..super appreciate it:)

Answer 29

\[\frac{dy}{dx}=\frac{-9(x-5)}{y+1}\]

y' = 0 when x = 5

and is undefined at x=-1

Answer 30

it =0 at 90/18 right if the derivative is -18x+90/2y+2

Answer 31

yes; which simplifies all the way down to 5

Answer 32

ohyea..oops..ur right..thnks a lottt

Answer 33

:) your welcome

Answer 34

Undefined at y=-1 and zero when x=5. You guys said that wrong like 4 times lol.