(5) (20p) Find and classify the critical points of f(x, y) = 7x - 8y +...
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 ?
Find the critical points of the function f(x)- f(x. y)x12xy+8y, determine the type of extrema (if any) and compute the function values at the critical points
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)
(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)
2. Find and classify all critical points for f(x,y) = -22 + y? (x - 8)
(1 point) Find and classify the critical points of)(x) = 7x*(3 - 2)* as local maxima and minima. Critical points: Classifications: (Enter your critical points and classifications as comma-separated lists, and enter the types in the same order as your critical points. Note that you must enter something in both blanks for either to be evaluated. For the types, enter min, max, or neither
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.
6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy. 6. [5 marks] Find and classify all stationary points of f(x,y) xy+2xy 7. [6 marks] Sketch the region of integration and evaluate the iterated integral 2 r2 JC 10 (y+xy-2) dxdy.
(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