Question

c. Does a cone with given volume and maximum surface area exist? Solve this 20. In Example 1, we found the maximum of f(x,y) = 2x + 5y on the ellipse (x/4)² + (y/3) = 1. problem again without using Lagrange multipliers. First, show that the ellipse is parametrized by X = 4 cost, y= 3 sin t. Then find the maximum value of f (4 cos t, 3 sin t) using single-variable calculus. Is one method easier than the other?

Answer 1

At first here I show that x=4cost , y=3sint are the parametric equation of the ellipse. Then I solved the problem.
thus the points are (1,4), (-3,-45) Again, @"(t) = -8 0031-15 sint at sint +15, last2 + 8% ie at the point ( 32, 45 Q"(t) = -8.15 - 15.8 q"(t) = -80-15:49 289 =-17 Lo 77 12 17. So, f/2,9) gives maximum at (e). Now, thus maximum alt) = 8.8 +15.15 17 289 2 17 17 Hence maximum of f(x,y) = maximum f L4 cst, 3.sint) 17. maximum of Plt) 217. So, fla,y) gives maximum valul 17 at the point 1950, 5) Obviously this method is easier than other
​​​​​​This method is easier than others method.