Proving 2nd Order Differential Eqns

[TannY]

Homework Statement

If y = (3x)/e^2x, find the value of x when d^2y/dx^2 = 0

Homework Equations

I'll just abbv d^2y/dx^2 as d2ydx2

The Attempt at a Solution

I kept getting stuck at:
d2ydx2 = 6/e^2
When d2ydx2 = 0,

6/e^2 = 0
6 = e^2

Then where's my x??

P.S: i have serious issues with differentiation =.=

 

[SunGod87]

y = 3x*e^(-2x)
y' = 3e^(-2x) - 6xe^(-2x)
y'' = -6e^(-2x) - 6e^(-2x) + 12xe^(-2x) = 0
-12e^(-2x) + 12xe^(-2x) = 0
12xe^(-2x) = 12e^(-2x)
x = 1

Differentiated using the chain rule (for exponentials) and product rule.

 

[TannY]

thanx! ^^
i thought that (e^2x)squared = (e^4x) lol

 

[ZioX]

thanx! ^^
i thought that (e^2x)squared = (e^4x) lol

It is.

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