2. Let f(x,y) = 2x2 - 6xy + 3y2 be a function defined on xy-plane (a) Find first and second partial derivatives of (b) Determine the local extreme points off (max., min., saddle points) if there are any. (c) Find the absolute max. and absolute min. values of f over the closed region bounded by the lines x= 1, y = 0, and y = x
2. For the two-argument function defined below: f(x,y) = 2x2 – 8xy + 5y + 3y2 (a) Find fx = and fex = . (5 marks) (b) Find fy = and fyy (5 marks) (c) Determine the critical point(s) of the f(x,y). (8 marks) (d) Find fxy (3 marks) (e) Determine each of the critical point(s) in the above (c) whether is a local minimum, local maximum or saddle point by using second partial derivative test. (4 marks)
How can the function x+11 x- x*y-lly, (x+y), f(x,y)= X-y be defined at the point (2,2) so that it becomes continuous at that point. Give a formula for the continuous extension to that point. Solve the question in the answer sheet. Insert the limit of the function at the point (2,2) in the text box:
(1 point) Find the maximum and minimum values of the function f(x, y) = 3x² – 18xy + 3y2 + 6 on the disk x2 + y2 < 16. Maximum = Minimum =
The equation y' 6x2 + 3y2 ту can be written in the form y' = f(y/x), i.e., it is homogeneous, so we can use the substitution u = y/x to obtain a separable equation with dependent variable u= u(x). Introducing this substitution and using the fact that y' = ru' + u we can write (*) as y' = xu'+u = f(u) where f(u) = Separating variables we can write the equation in the form dr g(u) du = where...
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For each of the following functions g determine if the corresponding functionf is continuous on the whole plane. Use "T" for true,"F" for false 2. g(x, y) 9x2y 3. gx, y)-4 sin) 4. g(x, y) xy sin(xy) 5. g(x, y) 3xy (1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For...
1. For the initial value problem y' = 3y2/3, y(2) = 0, there is a trivial solution, y(x) = 0. Find a nontrivial solution to this IVP. Does this contradict the existence theory for solutions of first onder IVPs y = f(x, y), y(x) = yo? Briefly explain. (VALUE: 4 l ations:
A probability function is defined by f(x)=(1/(square root 6pi))e^(-x^2)/2. Give the intervals where the function is increasing and decreasing.
WILL THUMBS UP IF DONE NEATLY AND CORRECTLY! Let X be a random variable with probability density function fx(2, -1 <z<3, 0 otherwise. Find the probability distribution of Y-X2 for 0 < y < 1, 1 < y < 9, and y > 9. [Obviously, fy(y)-0 for y < 0.1 Case 1: O < y < 1. Enter a formula below. Use * for multiplication, / for divison, ^ for power and sqrt for square root. For example, sqrt y...