# Linear Approximation

## Homework Statement

Let f(x,y) = $(xe^y)^8$

i) Find

$\frac{∂f}{∂x}$ $\frac{∂f}{∂y}$ $\frac{∂^2f}{∂x^2}$

ii) Using a tangent plane of f(x,y) find an approximate value of (0.98e^0.01)^8

## The Attempt at a Solution

i)
$\frac{∂f}{∂x}$ =$8e^{8y}x^{7}$

$\frac{∂f}{∂y}$ = $8x^{8}e^{8y}$

$\frac{∂^2f}{∂x^2}$ = $56e^{8y}x^{6}$

ii) I have done many questions on finding linear approximations but I have always had a function, a point to evaluate the function at and points to approximate it at.

In this I have the function Let f(x,y) = $(xe^y)^8$ and want to use it to approximate f(0.98,0.01) but I'm not sure at what point I should evaluate it at.

Can anyone help out?

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