2. Find and classify all critical points for f(x,y) = -22 + y? (x - 8)
(a) Find and classify all of the critical points of the function X f(x, y, z) = (x2 +42 + x2)3/2 on the unit sphere. (b) Find and classify all of the critical points of the function f(x, y, z) = x sin(x2 + y2 +22) on the sphere of radius
9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y) 9y3 + 3x2y-6y + 2 . 3. Find and classify all the critical points of f(x,y)
(8 points) Find all critical points and classify them via the second derivative test. (a) f(x,y) = 2.ry+y – 3y - 2 (b) f(x,y) = ye" – y? - I
QUESTION 7 Find all the critical points for f(x,y)=-x® + 3x - xy and classify each as a local maximum, local minimum or a saddle point. (9 marks)
(5) (20p) Find and classify the critical points of f(x, y) = 7x - 8y + 2xy - x + y®
consider the function f(x,y)=x^2-2xy+3y^2-8y (a)find the critical points of f and classify each critical point as local max min or saddle point (b) does f have a global max ?if so what is it ? does f have a global min ? if so what is it ?
5.1 (10 points): Let f(x,y) = 4 – 22 – y? Find all extrema (both relative and absolute) on the square D = {(x, y): 0 535 2,0 Sy <2}. 5.2 (10 points): Let f(x,y) = ry–2x+3y+100. Classify all critical points (rela- tive minimum, relative maximum, saddle point), and find the absolute maximum and absolute minimum on the triangle enclosed by the lines x = -4, y = 4, and y=++3.
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
(1 point) Consider the function f(x, y) = e-8x=x2-4y—y2 Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. fx = fxx = fxy =
Locate all critical points of f(x,y) and classify them as maxima, minima, saddle points or “none”.