SOLUTION: Hi, Please help me to find the extreme values of: {{{f(x,y)=x^2-y^2+3xy-x+2y+4}}}, where the partial derivative of f with respect to x is zero and the partial derivative of f with

Algebra ->  Functions -> SOLUTION: Hi, Please help me to find the extreme values of: {{{f(x,y)=x^2-y^2+3xy-x+2y+4}}}, where the partial derivative of f with respect to x is zero and the partial derivative of f with      Log On


   

Question 1117635: Hi,
Please help me to find the extreme values of: f%28x%2Cy%29=x%5E2-y%5E2%2B3xy-x%2B2y%2B4, where the partial derivative of f with respect to x is zero and the partial derivative of f with respect to y is also zero.
Thank you very much.



Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is nothing easier than that. 

1.  Take the derivative with respect to x and equate it to zero. You will get

    2x + 3y = 1.   (1)



2.  Take the derivative with respect to y and equate it to zero. You will get

    3x - 2y = -2.   (2)



3.  Solve the system of two linear equations (1) and (2) to get the answer

    x = -4%2F13,  y = 7%2F13.

You just are Calculus, correct ?

Should I explain to the person taking Calculus, how to solve a 2x2-system of linear equations ?