if x+y=8, find the max of x^y (Lambert W function)

If x+y=8 for nonnegative x and y, then find the maximum value of x^y. This question seems like a typical calculus optimization problem, but to find the exact answer, we will need to use the Lambert W function. https://youtu.be/Qb7JITsbyKs?si=lc0IZ6aTrvewRBIh Check out my 100 calculus 2 problems to help you with your calc 2 final: https://youtu.be/Kwyk_mteyNc?si=Dj_3rv2qeen7SiMi ---------------------------------------- 🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 💪 Get my math notes by becoming a patron: https://www.patreon.com/blackpenredpen #blackpenredpen #math #calculus #apcalculus