Question

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

Answer 1

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

Answer 2

*two answers

Answer 3

when you get the second derivative, factor out the \(e^{9x}\) and get
\[e^{9 x} (81 x^2+36 x+2)\]

Answer 4

\(e^{9x}\) is never zero, solve the quadratic equation you will get two zeros, those are the inflection points

Answer 5

Oh! Thank you! It's the quadratic function that I need to use for this problem.

Answer 6

And to find C and D would be by inputing it into which function?

Answer 7

I mean inputing the value of x.

Answer 8

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)

Answer 9

Thank you so much! This helps a whole lot!

Answer 10

yw