Let f(x,y) = 4 + x3 - 2y2. Find the gradient of f(x,y) at (1,1,3). Find the dire
ID: 1856160 • Letter: L
Question
Let f(x,y) = 4 + x3 - 2y2. Find the gradient of f(x,y) at (1,1,3). Find the direction in the xy plane that gives the steepest descent on the graph of f(x,y) away from the point (1,1,3). Find the critical points of the following fuvction f. Use the second Derivative Test (in two variable) to determine whether each critical point corresponds to a local maximum, local minimum, or saddle point. f(x, y) = x3 + y3 - 3xy + 5 Find the absolute maximum and minimum values AND where they occur, of the following function on the given closed sud bounded set R. Hint: Use Lagrange Multipliers to check for extreme points on the boundary f(x, y) = x2 - 2y2 R is the closed disk {(x,y): x2+y2 le 2} Find the equation of t he tangent plane to z exy + 2 at (0,1,3).Explanation / Answer
answer for first one df/dx=3x^2 =3 df/dy=-4y=-4 gradient(3,4) second one take dy/dx and then equate ir to zero u will get critical points and then second derivative negative-maximun positive-minimum for the last take again the gradient let it be a,b,c for df/dx,df/dy,df/dz a(x-point x coordinate)+b(y-point y coordinate)+c(z-point z coordinate)=0 is the answer
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