SOLUTION: Find the linearization of the function f(x,y)=sqrt(152−5x^2−2y^2) at the point (5, -3). L(x,y)= Use the linear approximation to estimate the value of f(4.9,

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Find the linearization of the function f(x,y)=sqrt(152−5x^2−2y^2) at the point (5, -3). L(x,y)= Use the linear approximation to estimate the value of f(4.9,      Log On


   

Question 1075836: Find the linearization of the function f(x,y)=sqrt(152−5x^2−2y^2) at the point (5, -3).
L(x,y)=

Use the linear approximation to estimate the value of f(4.9,−2.9) =
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

where df%2Fdx and df%2Fdy are the partial derivatives and are evaluated at (x%5B0%5D,y%5B0%5D).
So then,
f=sqrt%28152-5%2825%29-2%289%29%29=sqrt%289%29=3


So then,
L%28x%2Cy%29=+3-8.33%28x-5%29%2B2%28y-%28-3%29%29+
L%28x%2Cy%29=-8.33x%2B2y%2B50.65
So then,
f%28x%2Cy%29=+-8.33%284.9%29%2B2%28-2.9%29%2B5065
f%28x%2Cy%29=4.033 when the exact value is f%284.9%2C-2.9%29=3.89