Question

Find all points of inflection of the graph of the function f(x) = (1/12)x^4-2x^2+15

Answer 1

I found the first derivative to be (1/3)x^3-4x
And the second derivative to be x^2-4
And when f"(x) = 0, then x=2,-2

Answer 2

1) Find the first and second derivatives, f '(x) and f "(x).
2) Set f "(x) = to 0.
3) Solve the resulting equation. In this case you'll obtain 2 roots.
4) Determine whether the second derivative changes sign at either or both of these 2 roots.
If yes, you have an inflection point there; if no, you don't.

Pls show your work.

Answer 3

"Determine whether the second derivative changes sign at either or both of these 2 roots."
You mean plug in a number less than -2, between -2 and 2, and greater than 2 to see if theres a change in sign between these three values, right?

Answer 4

And if so, plug it into the original equation?

Answer 5

whats the second derivative?

Answer 6

I said that the second derivative is x^2-4
@mathmale
@karim728

Answer 7

Super easy...all you need is the 2nd derivative!!

f ' (x) = (1/3)x^3 - 4x
f '' (x) = x^2 - 4

now set the 2nd derivative equal to 0 and solve for x:

f '' (x) = 0 = x^2 - 4
x^2 = 4
x = + or - 2

You have two points of inflection: ( -2, f(-2) ) and ( 2, f(2) ). Be sure to substitute the value for x into the original equation to find your y.

Answer 8

Oh ok.
So I got (-2,25/3) and (2,25/3)
Oh thank you so much for your help, I was waiting so long.

Answer 9

No problem!! :)