1. Perform two iterations of the gradient search method on
f(x,y)= x^2+4xy+2y^2+2x+2y. Use (0,0) as a...
1. Perform two iterations of the gradient search method on
f(x,y)= x^2+4xy+2y^2+2x+2y. Use (0,0) as a starting point. Please
find the optimal λ* by taking the derivative and setting it equal
to 0.
Let f(x, y) = xy3 − x 2 + 2y − 1. (a) Find the gradient vector
of f(x, y) at the point (2, 1).
(b) Find the directional derivative of f(x, y) at the point (2,
1) in the direction of ~u = 1 √ 10 (3i + j).
(c) Find the directional derivative of f(x, y) at point (2, 1)
in the direction of ~v = 3i + 2j.
The Vector Field f(x, y) = (2x + 2y^2)i + (4xy - 6y^2)j has
exactly one potential function f (x, y) that satisfies f(0, 0).
Find this potential function , then find the value of this
potential function at the point (1, 1).
Consider the function f(x, y) = 4xy − 2x 4 − y
2 .
(a) Find the critical points of f.
(b) Use the second partials test to classify the critical
points.
(c) Show that f does not have a global minimum.
For the function f(x,y) = 4xy - x^3 - 2y^2 find and label any
relative extrema or saddle points. Use the D test to classify. Give
your answers in (x,y,z) form. Use factions, not decimals.
-- Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01)
-- find Zvu for z= f(x,y), x=uv , y= v^2 + u^2
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