Question

use the 2nd derivative test to find all the local maxima, local minima, and saddle points of the function f(x,y)= 4xy - x^4 - 2y^2

Answer 1

I know you have to find the derivatives with respect to x and y and then xy. ... then you find the 2nd derivative of the 3 and from here I am lost.

Answer 2

\[fx= 12x ^{2} \] and \[fy= 4x - 4y \] and finally \[f2xy= 4y-4x ^{3} = 4\]

Answer 3

your \(f_x\) is not correct

Answer 4

oops .... its \[4y - 4x ^{^{3}} \] ... the first equation is actually fxx.

Answer 5

\[f_{xx}=-12x^2\]