[-/8.33 Points] DETAILS MY NOTES LARCALC12 13.10.005.EP. Consider the following and assume that both x and y are positive. f(x, y) = x² + y² g(x, y) = x + 2y - 10 Find the following gradients. Vf(x, y) = Vg(x, y) = Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. minimize f(x, y) = x² + y² constraint: g(x, y) = x + 2y - 10 = 0

The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02

How are the absolute maximum and minimum similar to and different from the local extrema?

Find all points where the functions have any relative extrema. Identify any saddle points. f(x,y)=x2+xy2x2y+2