The function f(x) = (9 x+2)e^{-6 x} has one critical number. Please help me find the critical number!

1 answer

I read that as

f(x) = (9x + 2) e^(-6x)

f ' (x) = (9x + 2)( e^(-6x) )(-6) + 9 e^(-6x)
= 0 for max/min (critical values)

e^(-6x) [ -6(9x + 2) + 9] = 0

e^(-6x) = 0 ---> no solution
or
-54x -12 + 9 = 0
x = -1/18

if you include the x-intercepts in your critical values
then 9x+2=0
x = -2/9

y-intercept, let x = 0
y = 2 e^0 = 2

Wolfram agrees with me
http://www.wolframalpha.com/input/?i=plot++%289x%2B2%29e%5E%28-6+x%29