Jusaquikie
  • Jusaquikie
trying to find an infliction point. the rest i'll make neat.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Jusaquikie
  • Jusaquikie
\[f(x) = x^2e^{-x}\] \[f'(x) =e^{-x}(2x-x^2)\] \[f'' =e^{-x}(x-2)^2\] or \[f'' =e^{-x}(x^2-4x+2)\]
hartnn
  • hartnn
\(f'' =e^{-x}(x^2-4x+2)\) is correct \(f'' =e^{-x}(x-2)^2\) is incorrect
Jusaquikie
  • Jusaquikie
for my infliction points i need f"=0 i thought this should be at 2 but that is not right. when i solve f" for x on my calculator i get \[-(\sqrt{2}-2) \]and \[\sqrt{2}+2 \]

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hartnn
  • hartnn
x^2-4x+2 will get u to correct points
Jusaquikie
  • Jusaquikie
i believe this has something to do with it being squared but i don't understand why beacuse 0 squared is still 0
Jusaquikie
  • Jusaquikie
i know the answer is the first of the infliction points i have listed but i just don't see how to solve the second derivitive that way
Jusaquikie
  • Jusaquikie
well how to solve f"=0 that way
hartnn
  • hartnn
what exactly is your doubt ? u got \(f'' =e^{-x}(x^2-4x+2)\) now f''(x)=0 will give \((x^2-4x+2)=0\) can u solve this quadratic to get 2 values of x ?
hartnn
  • hartnn
those 2 values of x will be your inflection points.
Jusaquikie
  • Jusaquikie
do i need to use the quadratic formula? beacuse it simplifies to (x-2)(x-2) so 2 will make it zero
hartnn
  • hartnn
@Jusaquikie plz observe that \(f'' =e^{-x}(x-2)^2\) IS INCORRECT !
hartnn
  • hartnn
and you use quadratic formula for \(x^2-4x+2=0\)
hartnn
  • hartnn
or u could complete the square
Jusaquikie
  • Jusaquikie
ok i see now that for (x-2) to work it would have to be X^2 - 4x +4
hartnn
  • hartnn
yes!
Jusaquikie
  • Jusaquikie
it's just late and my mind is jumping to the easiest answer after computing that beastly second derivatives.
Jusaquikie
  • Jusaquikie
so the quadratic formula would be what i'd use if they didn't come out even and if i used that i bet i'd get the right answer
Jusaquikie
  • Jusaquikie
thanks for the help @hartnn
hartnn
  • hartnn
thats correct.
hartnn
  • hartnn
welcome ^_^
Jusaquikie
  • Jusaquikie
now i can sleep
hartnn
  • hartnn
good night and sweet dreams :)

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