Question

Clac 3 Linearization: Find the Linearization of the function f(x,y,z)=sqrt(2x^2+3y^2+z^2) at (2,3,3).
My work: I found that f(2,3,3)=sqrt(44)
df/dx=8+(1/(2sqrt(44)))
df/dy=18+(1/(2sqrt(44)))
df/dx=6+(1/(2sqrt(44)))
so the linearization=sqrt(44)+((8+(1/(2sqrt(44))))(x-2))+((18+(1/(2sqrt(44))))(y-3))+((6+(1/(2sqrt(44))))(z-3)).
I am being told that this is incorrect and was trying to figure out why

Answer 1

\[(x,y,z)= \sqrt{(2x^2+3y^2+z^2)}\,\,\,\,\,at (2,3,3).\]
Hey linearization is a linear function in all the three variables. What is ur soln ?

Answer 2

are you saying that sqrt(44)+((8+(1/(2sqrt(44))))(x-2))+((18+(1/(2sqrt(44))))(y-3))+((6+(1/(2sqrt(44))))(z-3)) needs to be simplified more?

Answer 3

I am saying the linearization is not a number neither three numbers it is a linear
\[\color{red}{\frak{Function}}\]

Answer 4

humm ok so what should i be looking for?

Answer 5

the numbers 8, 18,, 6 are \[\color{yellow}{MULTIPLIERS,\,\,\,NOT\,\,\,\,SUMMANDS}\]

Answer 6

THEY ARE 3 "SLOPES", so to say

Answer 7

instead of "+" it should be "*" after each of them, meaning multiplication

Answer 8

after each of what?
the 8,16,6?

Answer 9

\[ df/dx=8(1/(2sqrt(44)))\]

Answer 10

got it lol
for some reason i was thinging +'s

Answer 11

just realized what was going on.
Tyvm lol

Answer 12

what is tyvm ?

Answer 13

thank you very much

Answer 14

thx 4 xplnshn

Answer 15

for some reason i thinking chain rule added the parts together

Answer 16

It is rather \[ \Huge CENTRAL\quad that\\ \Huge \,\,\, MULTIPLICATION\]

Answer 17

What is the level and "year" you are studying this material in ?

Answer 18

@BenBlackburn ?

Answer 19

sophmore 2nd in college. its just been awhile. over the summer i took linear algebra and we did not do much of this stuff in clac 2. so some of this stuff is causing me to go back and refresh my memory

Answer 20

so some careless errors are popping up

Answer 21

Well the lecturer should have stressed 200 times the chain rule

Answer 22

it is in fact deeply intertwined with the idea of LINEARIZATION
look suppose y = K*x and z = M*y ===> obviously z = K*M*x

Answer 23

the same with derivatives !

Answer 24

Well good luck & farewell.

Answer 25

haha ty you too