## Jusaquikie Group Title trying to find an infliction point. the rest i'll make neat. one year ago one year ago

1. Jusaquikie Group Title

$f(x) = x^2e^{-x}$ $f'(x) =e^{-x}(2x-x^2)$ $f'' =e^{-x}(x-2)^2$ or $f'' =e^{-x}(x^2-4x+2)$

2. hartnn Group Title

$$f'' =e^{-x}(x^2-4x+2)$$ is correct $$f'' =e^{-x}(x-2)^2$$ is incorrect

3. Jusaquikie Group Title

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 $\sqrt{2}+2$

4. hartnn Group Title

x^2-4x+2 will get u to correct points

5. Jusaquikie Group Title

i believe this has something to do with it being squared but i don't understand why beacuse 0 squared is still 0

6. Jusaquikie Group Title

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

7. Jusaquikie Group Title

well how to solve f"=0 that way

8. hartnn Group Title

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 ?

9. hartnn Group Title

those 2 values of x will be your inflection points.

10. Jusaquikie Group Title

do i need to use the quadratic formula? beacuse it simplifies to (x-2)(x-2) so 2 will make it zero

11. hartnn Group Title

@Jusaquikie plz observe that $$f'' =e^{-x}(x-2)^2$$ IS INCORRECT !

12. hartnn Group Title

and you use quadratic formula for $$x^2-4x+2=0$$

13. hartnn Group Title

or u could complete the square

14. Jusaquikie Group Title

ok i see now that for (x-2) to work it would have to be X^2 - 4x +4

15. hartnn Group Title

yes!

16. Jusaquikie Group Title

it's just late and my mind is jumping to the easiest answer after computing that beastly second derivatives.

17. Jusaquikie Group Title

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

18. Jusaquikie Group Title

thanks for the help @hartnn

19. hartnn Group Title

thats correct.

20. hartnn Group Title

welcome ^_^

21. Jusaquikie Group Title

now i can sleep

22. hartnn Group Title

good night and sweet dreams :)