Inflection points?: f(x)= (3/4)x^4 - x^3 - 3x^2 + 6x

Question

anonymous · Answer

1. Find the inflection points. Show why there are exactly two inflection points for this function.

hartnn · Answer

to get inflection points, we equate 2nd derivative of the function to 0 
f''(x) =0 

so can you first find f''(x) ??

anonymous · Answer

F’’(x) = 9x^2 – 6x + 6

hartnn · Answer

+6 ? or -6 ?`

anonymous · Answer

Oh, sorry! f''(x) = 9x^2-6x-6

hartnn · Answer

yes, now solve 
9x^2-6x-6=0

anonymous · Answer

I know that we have to factor 9x^2-6x-6, but I'm not very sure how to factor it. Another person had helped me with a similar question the other day and he had group factored it. Not sure which way to go?

anonymous · Answer

When I factor it, I get 3(3x^2 - 2x -2)

hartnn · Answer

you'll need quadratic formula
know what that is ?
(solutions are irrational)

anonymous · Answer

Yes, I do. okay, give me one quick moment to plug in my numbers.

hartnn · Answer

sure, take your time :)

anonymous · Answer

6 +/- (sqrt(-6^2 – 4(9*-6)))/2(9)
=6 (sqrt(36 – 216) / 18)
= 4.47

anonymous · Answer

is this correct?

hartnn · Answer

naah...
b^2- 4ac = (-6)^2 - 4 (9)(-6)  = 36 + 216
....

anonymous · Answer

Yea, realized I was way off. I'm going to try and solve it in a different way. one sec.

hartnn · Answer

x = 1/3 – 1/3sqrt(7)
x = 1/3 + 1/3sqrt(7)

hartnn · Answer

YES

anonymous · Answer

Okay, lol. thank you.

hartnn · Answer

welcome ^_^