Question

how to do part A B and C?

Use Lagrange multipliers to find the maximum and minimum values of the function f subject to the given constraints g and h f(x, y, z)-yz-6xy; subject to g : xy-1-0 h:ỷ +42-32-0 and a) (i)Write out the three Lagrange conditions, i.e. Vf-AVg +yVh Type 1 for A and j for y and do not rearrange any of the equations Lagrange condition along x-direction: Lagrange condition along y-direction: Lagrange condition along z-direction: 0.5 0.5 0.5 (ii) Find the exact value of / and use this to rewrite the Lagrange condition in the y-direction. 0.5 Lagrange condition along y-direction: 0.5 (iii) Write out the condition along the z-direction after eliminating J. (Rearrange to avoid any divisions in your equation.) Lagrange condition along z-direction: (iv) Use the relation found in (ii) and one of the constraints to find y2 1 1 b) Find all the points at which f has extreme values subject to the constraints g and h as above. (i Which combination of the following sets contains these critical points? Each part worth of a mark (ii) How many points are there in total? 02 04 08 016 1 c Find maximum and minimum values of f fmax = 1 1 min =

Answer 1

Soltion '- jiren dala'- La Ta?ge Condition along χ_divect! tion Abng y- diaection 2 Abng -direction = 0 + 82山 84 2

46 4- And cwhen tJrng 4+1-0 ihen u.

So u aet ctical Points aj 4- 4 2 Co When 2-2 When 22 -オ darn Coe get csictial Points

4- maximum value Max F17