17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.
5. Find the absolute max and absolute min of f(:1, y) = x2 + 2y2 – 2.0 – 4y on the rectangle (<r<2,0 <y<3.
please solve now (a) 3 marks The directional derivative of f(x,y) at a point P in the direction of the vector <2,3 > equals 7, and the directional derivative of f(x,y) at a point P in the direction of the vector < 1,-2 > equals 5. Find Vf at P. (b) 4 marks (c) 4 marks Find Zxy if z3 = xz+y. (d) 4 marks Find and classify all local extreme points of f(x,y) = x3 + y3 - 3x...
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) =?
The directional derivative of the function f(x, y) = 2x In(y) in the direction v =< 0,1 > at the point (1,1) is equal to 2. Select one: O True False
5. If two random variables X and Y have the joint density k(52+2y2) for 0<<2 0 <y< 1 f(r, y) elsewhere (a) Find k (b) Find P(0<x< 1, 0<Y<0.5) (c) Find marginal density fi(a) and f2(y) (d) Are X and Y independent? (e) Find E(X) () Find P(X2 0.5). expression for fi(x|y); (g) an
U Question 22 1 pts Find the absolute minimum of f(x, y) = x2 + 4y? - 2x²y + 4 on the square given by -1 << < 1 and -1<y<1. 11 4 8 None of the above or below O-2 07
3 U + tyy = 0. 3. Find the directional derivative of f(x,y) 2In y at the point P(2,1) in the direction ū= 21+ 4. Find the linearization of f(x,y) = x2 + y2 at the point P(3, 4) and use it to
Find the directional derivative D−→ u f(x,y) of the function f(x,y) = x2 + 3xy + y3 where →− u is the unit vector given by angle θ = π 4. What is D−→ u f(1,1)?
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney, if 0 < x < f(z, y) = otherwise. Find P(X > 1|Y = y)