Critical point Question (I really need help. Please!) ASAP!

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thomcart8

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Okay my problem wants me to find the value at a so that the function f(x) = xe^ax has a critical point at x = 3. Okay I think the derivative is (xa+1)e^xa. So if I substitute 3 in for x and set the equation to (3a+1)e^3a = 0 i should the value for a i think. I dont know am i even doing this right?
 
Re: Critical point Question (I really need help. Please!) AS

\(\displaystyle f(x) \ = \ xe^{ax}\)

\(\displaystyle f'(x) \ = \ e^{ax}+axe^{ax} \ = \ e^{ax}(1+ax)\)

\(\displaystyle ax \ = \ -1, \ x \ = \ \frac{-1}{a} \ = \ 3, \ hence \ a \ = \ \frac{-1}{3}.\)

\(\displaystyle f(x) \ = \ xe^{-x/3}, \ f(3) \ = \ 1.1036383 \ = \ critical \ point \ = \ max.\)
 
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