The function f(x, y) = 10−x 2−4y 2+2x has one critical point.
Find that critical point and show that it is not a saddle point.
Indicate whether this critical point is a maximum or a minimum, and
find that maximum or minimum value.
Let f(x, y) = x^ 2 + kxy + 4y^ 2 , k a constant. The point (0,
0) is a stationary point of f. For what values of k will f have a
local minimum at (0, 0)?
(a) |k| > 4
(b) k ≥ −4
(c) k ≤ 4
(d) |k| < 4
(e) none of the above
The point P : (2, 2) is a stationary point of the function f(x,
y) = 6xy − x ^3...
Undetermined Coefficients:
a) y'' + y' - 2y = x^2
b) y'' + 4y = e^3x
c) y'' + y' - 2y = sin x
d) y" - 4y = xe^x + cos 2x
e) Determine the correct form of a particular solution, do not solve
y" + y = sin x
Consider the optimization problem of the objective function f(x,
y) = 3x 2 − 4y 2 + xy − 5 subject to x − 2y + 7 = 0. 1. Write down
the Lagrangian function and the first-order conditions. 1 mark 2.
Determine the stationary point. 2 marks 3. Does the stationary
point represent a maximum or a minimum? Justify your answer.