Question

f(x,y)=4x-3y function on the curve x^2+y^2=25 when finding the extreme values using Lagrange multipliers which of these statements are true?

1)f is at minimum value at (-4,-3) on this curve
2)f is at maximum value at (4,3) on this curve
3)maximum value of f is 25 on this curve
4)f has not got any extremum points on this curve

Answer 1

Given, function finger 4x-3y google tye - 25 subjected to solution: Take all will the partial derivatives which for the Lagrange multiplier be Needed equations: fx = 4 2x = - 3 fy Ja = gy = 2y Multiplier equations: up the setting 4= xen Lagrange fu= ago fyny egaco) eq" (2) -3= =rzy x’+y?=25 eq03) constraint: Taking eq "(1) eqn(2)

wl A 11 ४. ਹੈ - wo eq"14) y → 3 4 x into eqh (3) to find: substituting x +39=25 ? 2 น + 9x² = 25 介 16 25ne = 25 16 = > u= 4 Now, from eq? (4) = -3 for 2=4 , y = -2 (4) 3 for a=-4, y = *(-4) the solution: (21.9) values we get (4,-3) & (-4,3) by simply simply finding their Now, into fin,y) : when plugging

• f14,-3) = 4(4) – 36-3) = 16+9 = 25. • f(-4,3) 41-4) - 3/3) = -16-9= -25. at (4,-3) so, the value = 25 Maximum value = -25 at 1-4, 3) & the Minimum