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