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Find the inflection points at x=C and x=D with C less than or equal to D? Consider the function f(x) = x^(2)e^(9x). I just don't know how to determine what the inflection points are after I find the second derivative. f(x) has two inflection points at x = C and x = D with C less than or equal to D What is C What is D

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take the derivative twice, set it equal to zero, there are to answers one is smaller than the other, the smaller one is C and the larger one is D
*two answers
when you get the second derivative, factor out the \(e^{9x}\) and get \[e^{9 x} (81 x^2+36 x+2)\]

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Other answers:

\(e^{9x}\) is never zero, solve the quadratic equation you will get two zeros, those are the inflection points
Oh! Thank you! It's the quadratic function that I need to use for this problem.
And to find C and D would be by inputing it into which function?
I mean inputing the value of x.
exactly you get two answers from the quadratic formula the smaller one C and the larger on D if you have to write both coordiates, yes, you evaluate the function at those points (the original function)
Thank you so much! This helps a whole lot!

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