Thread: Point of Inflection (second derivative)- easy

Can anyone solve this one?
I got stuck..

f(x) = 4/ (x^2 + 8)

I need f''(x) second derivative for this

Originally Posted by dkssudgktpdy

Can anyone solve this one?
I got stuck..

f(x) = 4/ (x^2 + 8)

I need f''(x) second derivative for this

Can you get the first derivative? Please show all your work.

Originally Posted by mr fantastic

Can you get the first derivative? Please show all your work.

yup.
f(x) = 4 (x^2 +8)^-1

= -4 (x^2 +8)^-2 (2x)

= -8x (x^2 +8)^-2
f''(x)= 16x (x^2 +8)^-3 (2x)
= 32x (x^2 +8)^-3
0 = 32x/ (x^2 +8)^3
x=0

and.. 0 is not the right answer. Where did I make a mistake?

Originally Posted by dkssudgktpdy

yup.
f(x) = 4 (x^2 +8)^-1

= -4 (x^2 +8)^-2 (2x)

= -8x (x^2 +8)^-2
f''(x)= 16x (x^2 +8)^-3 (2x)
= 32x (x^2 +8)^-3
0 = 32x/ (x^2 +8)^3
x=0

and.. 0 is not the right answer. Where did I make a mistake?

You need to use the product rule or quotient.

Originally Posted by TheEmptySet

You need to use the product rule or quotient.

I got it.
Thank you!