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- How are the absolute maximum and minimum similar to and different from the local extrema?Find the absolute minimum and absolute maximum of f(x,y)=19−9x+13y on the closed triangular region with vertices (0,0),(13,0) and (13,15). Minimum value: Occurs at: Maximum value: Occurs at:Find the exact location of (a) a relative maximum at (x,y)=_____ From: f(x)=2x^2-8x+2 with domain [0,3]
- Find the orthogonal trajectories for the family of curves (enter your solution in the form: F(x,y)=c or y=F(x,C) Where C is a needed constantWhat value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and the value of the maximum rate of decrease.
- Find the critical point of the function f(x,y)=6x−2y^2−ln(|x+y|). c=Use the Second Derivative Test to determine whether it isA. a saddle pointB. a local maximumC. test failsD. a local minimumFind the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x >0, y>0) and show that ƒ takes on a minimum there.This multfunction apparently has a local maximum in addition to a local minimum and two saddle points. I cannot find the local maximum, please show work and explain.