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Find the linear approximation of each function at the indicated point.$$f(x, y)=x \sqrt{y}, \quad P(1,4)$$

$L(x, y)=2 x+\frac{1}{4} y-1$

Calculus 1 / AB

Calculus 3

Chapter 4

Differentiation of Functions of Several Variables

Section 4

Tangent Planes and Linear Approximations

Functions

Partial Derivatives

Functions of Several Variables

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were given a function were asked to find a linear approximation at an indicated point to the function you have the f of X y equals expert why and the point is 14 Find linear approximation. We had a partial derivative. If x X Y is equal to why and if, why. Six y is equal to 1/2 X white in the negative 1/2 which is simply X over two y So we have that half of 14 is equal to one times. Route four, which is to FX of 14 is equal to to and F y of 14 is equal to one over two times two or 1/4. And so the linear approximation at this point elects Why is given by to plus two times X minus one plus 1/4 times Y minus four. We can simplify as two x plus 1/4 y and then to minus two minus one. So our answers Alex Wise to X plus 1/4 Y minus one

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