Thread: [SOLVED] Optimization in Several Variables

F(x,y) = (2*y+1)*e^(x^2-y)
Find critical point and prove there is only one.
Use second derivative test to determine nature of crit. pt.


I know the procedure in solving it: set partial derivatives to zero and solve resulting equations. And by second derivative test, if D>0, f(a,b) is local min/max; D<0, (a,b) is saddle point. if f_xx(a,b)>0, f(a,b) is min
where D=D(a,b)=f_xx(a,b)f_yy(a,b)-f_xy(a,b)^2

I have no idea how to get the partial derivatives and start the problem. Any help will be appreciated, thanks.

Originally Posted by coe236

F(x,y) = (2*y+1)*e^(x^2-y)
Find critical point and prove there is only one.
Use second derivative test to determine nature of crit. pt.


I know the procedure in solving it: set partial derivatives to zero and solve resulting equations. And by second derivative test, if D>0, f(a,b) is local min/max; D<0, (a,b) is saddle point. if f_xx(a,b)>0, f(a,b) is min
where D=D(a,b)=f_xx(a,b)f_yy(a,b)-f_xy(a,b)^2

I have no idea how to get the partial derivatives and start the problem. Any help will be appreciated, thanks.

The exponential function is never zero, hence



Again exponential never zero, so:

Surely ou can continue from there?

yup, that simplified things a lot. Thank you