Question

Hello! Could somebody tell me how can I linearizing a second order non-linear equation?
So I have f(x,y)= xy. Can I make a linear approximation on the f(x,y) function?
Thank you!

Answer 1

y = f(a) + f '(a) (x - a)

Answer 2

is this tangent to f ?

Answer 3

yes

Answer 4

thank you!

Answer 5

its actually,
\(\large f\left(x,y\right)\approx f\left(a,b\right)+\frac{\partial f}{\partial x}\left(a,b\right)\left(x-a\right)+\frac{\partial f}{\partial y}\left(a,b\right)\left(y-b\right).\)
for 2 variables.

Answer 6

y = f(a) + f '(a) (x - a) applies only for f(x) as the function of x only....

Answer 7

here u get
\(\huge \frac{\partial f}{\partial x}=y \\\huge \frac{\partial f}{\partial y}=x \)

Answer 8

so,
\(\huge \frac{\partial f(a,b)}{\partial x}=b \\\huge \frac{\partial f(a,b)}{\partial y}=a \\ f(a,b)=ab\)
now just plug in values.

Answer 9

@silvia

Answer 10

@hartnn thank you!

Answer 11

welcome ^_^