find the linear approximation of the funtion f(x,y )= sqrt 20-x^2-7y^2 at (2,1). use your answer to aproximate f(1.95, 1.08)

Question

dumbcow · Answer

http://en.wikipedia.org/wiki/Linear_approximation a=2 b=1 then find partial derivatives wrt x and wrt y sub everything into formula

anonymous · Answer

f (2,1)+ sqrt 2x (x+2) +  sqrt 14y ( y-1)

dumbcow · Answer

why is it sqrt(2x) ?

is everything inside radical?

anonymous · Answer

yes

anonymous · Answer

i think is 1/2 ( 2x) ^-1/2

anonymous · Answer

1/ sqrt 2x

dumbcow · Answer

hmm
$$d/dx \sqrt{20-x^{2}-7y^{2}} = \frac{-2x}{2\sqrt{20-x^{2}-7y^{2}}} =  \frac{-x}{\sqrt{20-x^{2}-7y^{2}}}$$

anonymous · Answer

ok forget about that

anonymous · Answer

$$d/dy = -7y/\sqrt{20-x^2-14y^2}$$

dumbcow · Answer

right

dumbcow · Answer

oh should still be 7y^2 in radical

dumbcow · Answer

after plugging in (2,1)
i get

$$f(x,y) \approx 3-\frac{4}{3}(x-2)-\frac{7}{3}(y-1)$$

anonymous · Answer

@dumbcow after that i need to  aproximate f(1.95, 1.08) doing the same thing that we did with (2,1)

dumbcow · Answer

no we already have the linear approximation
plug in (1.95,1.08) for (x,y)

anonymous · Answer

@dumbcow  ok