Question

Find the inflection points of f(x)=x^4+x^3-45x^2+2.

Answer 1

You know that points of inflection occur when the 3rd derivative equals zero: take the third derivative, set it equal to zero, and that's your answer.

Answer 2

Would the first derivative be: F'(x)= 4x^3+3x^2-45(2x) ?

Answer 3

You have to find the roots of the 2nd derivative not the third one..

Answer 4

@DrakeNetherlands , no. And @LeightnerRach yes.

Answer 5

Oh wait, yes, its 2nd, not third.

Answer 6

I'm not sure what the second derivative is suppose to be.. Is it 12x^2+6x+90?

Answer 7

That's it; not set it equal to zero, and try to factor out. If you don't want to attempt; use quadratic formula.

Answer 8

And your second derivative should be 12x^2+6x-90 and then you set it equal to 0 and you're done
which should be -3 and 5/3 correct me if I'm wrong :)

Answer 9

Yeah, it doesn't factor out; use QF.

Answer 10

Would you factor a 6 out first and use the equation: 2x^2+x-15 in the quadratic formula?

Answer 11

Umm, I wouldn't, imo, but you can if you wish. I'm not too sure if you have to re-multiply the end result by the number you factored or not, is the reason I don't.

Answer 12

Okay, thank you!

Answer 13

Yw, feel free to ask anymore questions if needed; I'm glad to help. :)