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anonymous
 5 years ago
Suppose that x=2 is a critical point of f(x)=x^(3)e^(−kx). Find the value of k:
anonymous
 5 years ago
Suppose that x=2 is a critical point of f(x)=x^(3)e^(−kx). Find the value of k:

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You could derive using the product rule (x^3)'(e^kx)+(x^e)(e^kx)', and set that equal to 0 and plug 2 in for every x to solve for k.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the answer would be?? i really need the answer now :/

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.03x^2(e^kx)+(x^3)(ke^kx) = 0 3*2^2*(e^2k)+(2^3)(ke^2k) = 0 12e^2k+8ke^2k = 0 e^2k(128k) = 0 ln(e^2k)+ln(128k) = 0 2k+ln(128k) = 0 solve with a calculator? Someone please stop me if I'm doing it wrong. It's late.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[12e^{2k}  8ke^{2k} =0 \rightarrow e^{2k}(12  8k) = 0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0either e^(2k) = 0 or 128k = 0 => k = 12/8

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0other solution is k = 0, I suppose

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is there any other restrictions? f(2) gets a bigger value when k = 0. I don't know if that's relevant

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no i think 12/8 was the answer . thank you :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0They both seem correct
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