Find the formula for a function of the form y=bxe^(-ax) with a local maximum at (4,12)...

Answer 1

y' = b(1-ax)e^(-ax)
1-ax=0, at x=1/a = 4, making a = 1/4

y(4) = 4be^(-4/4) = 12
4b/e = 12
b = 3e

y = 3ex e^(-x/4)

verify this at

https://www.wolframalpha.com/input/?i=y%3D3ex+e^%28-x%2F4%29