Find a formula for a function of the form y=bxe^(−ax) with a local maximum at (6,1). a= b=

Answer 1

y' = be^-ax - abxe^-ax = 0; e^-ax(b - abx) = 0; x = 1; e^-a(b - ab) = 0; b - ab = 0; b(1 - a) = 0

y(1) = be^-a = 6; a = 1; be^-1 = 6; b = 6e;

Then y' = 6e^1-x - 6xe^1-x; y'' = [6e^1-x(1 - x)]' = - 6e^1-x(1 - x) - 6e^1-x = - 6e^1-x(2 - x).

So, y''(1) = - 6 < 0. So, nwe have maximum at (1, 6) and a = 1, b = 6e

Answer 2

y = bxe^-ax y' = be^-ax (1-ax)

1) Plug point (x,y) = (6,1) into equation: 1 = 6be^-6a

2) Now plug in y' = 0 at the same x value: 0 = be^-6a(1-6a) or a=1/6

Plug a into 1st equation to solve for b. The 1st derivative changes sign from + to -, so you know it's a max crit. pt.

You can plot the equation with your constants using Desmos and you will see that the point (6,1) is a max.

Please consider a tutor.