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