1. The problem statement, all variables and given/known data Let f(x,y) = [itex](xe^y)^8[/itex] i) Find [itex]\frac{∂f}{∂x}[/itex] [itex]\frac{∂f}{∂y}[/itex] [itex]\frac{∂^2f}{∂x^2}[/itex] ii) Using a tangent plane of f(x,y) find an approximate value of (0.98e^0.01)^8 2. Relevant equations 3. The attempt at a solution i) [itex]\frac{∂f}{∂x}[/itex] =[itex] 8e^{8y}x^{7}[/itex] [itex]\frac{∂f}{∂y}[/itex] = [itex] 8x^{8}e^{8y}[/itex] [itex]\frac{∂^2f}{∂x^2}[/itex] = [itex] 56e^{8y}x^{6}[/itex] 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) = [itex](xe^y)^8[/itex] 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?
Was leaning towards that, just wanted to make sure. That all worked out nicely, thanks for your advice =D