In Example 1, we found the maximum of (x, y) = 2x + 5y on the ellipse

In Example 1, we found the maximum of ƒ(x, y) = 2x + 5y on the ellipse (x/4)² + (y/3)² = 1. Solve this problem again without using Lagrange multipliers. First, show that the ellipse is parametrized by x = 4 cos t, y = 3 sin t. Then find the maximum value of ƒ(4 cos t, 3 sin t) using single-variable calculus. Is one method easier than the other?

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EXAMPLE 1 Find the extreme values of f(x, y) = 2x + 5y on the ellipse (-) + (-) = 1