1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points. 1. (25 points) Let f (x, y) = x4 - 4xy + y2 (6 points) Find fr.fy a. b. (9 points) Find fxx fry, fry c. (6 points) Find all critical points.
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y
Calculate the work done by the vector field F?(x, y?)= ?(4xy, 2x^2) ? along a smooth and simple curve from point (?3, −1)? to point (?4,2)?.
Vector Fields problems. Question 6 Let f (x, y) = x3 + 4xy + 2y2 and of =<P,Q >. P (2, 1) = ? Question 7 vf same as in Question 6 Q (2, 1) =?
6. Let f(x,y) = 1 if 0 < y < 2x, 0<x<1, and 0 otherwise. Find the following: a) f(y|x) b) E(Y|X = x) c) The correlation coefficient, p, between X and Y
4. Let f(x, y) = 2 - 2x – y + xy. (a) Find the directional derivative of f at the point (2,1) in the direction (-1,1). [2] (b) Find all the critical points of the function f and classify them as local extrema, saddle points, etc. [2]
14. Find product: (2x +y)(2x - y) 15. Factor: 4xy +2y 6x + 3 2 16.Factor: 36x2- 4y
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
24. Let X and Y be continuous random variables with joint density function 4xy for 0 < x, y 1 f(x, y) otherwise. What is the probability of the event X given that Y ?
x2–2x-3 Let f(x) = Find the X-value(s) for which the graph of y = f(x) has a horizontal tangent line. x+2