PREP Quickstart, Multivariable Calculus Sage Quickstart for ...

↦ 2 x + y − 6(x,y)↦ x + 2 y(x,y)f xxD = 3f xxf xx2/20/13 PREP Quickstart, Multivariable Calculus -- SageQuiz: Why did we not need to declare the variables in this case?fx(x,y)= f.diff(x)fy(x,y) = f.diff(y)fx; fyf.gradient()solve([fx==0, fy==0], (x, y))(x,y) ↦ (2 x + y − 6, x + 2 y)H = f.hessian()H(x,y)[[x = 4,y = (−2)]]2112And of course if the Hessian has positive determinant andis positive, we have a local minimum.( )Notice how we were able to use many things we've done up to now to solve this.MatricesSymbolic functionsSolvingDifferential calculusSpecial formatting commandsAnd, below, plotting!html("$f_{xx}=%s$"%H(4,-2)[0,0])html("$D=%s$"%H(4,-2).det())= 2And of course if the Hessian is positive definite andis positive, we have a local minimum.Notice how we were able to use many things we've done up to now to solve this.test.sagenb.org/home/Carlos_Rodriguez/20/print 7/9