Question

The second derivative of g(x)=x^2-27/x(x>0) changes sign at the point x= ?

Answer 1

can u use the equation editor so that makes more sense?

Answer 2

is it
\[g(x)=\frac{x^2-27}{x} or g(x)=x^2-\frac{27}{x}?\]

Answer 3

sorry.The second one is correct.

Answer 4

\[g'(x)=2x + \frac{27}{x^2}\]

Answer 5

g'(x)=2x+(27/x^2 )
is this what you got for the fist derivative?
then
we need to find g''
g''(x)=2-(2*27/x^3)

Answer 6

\[g''(x)=x-\frac{27*2}{x^3}\]

Answer 7

now set g''=0
\[\frac{2x^3-2*27}{x^3}=0\]
\[\frac{x^3-27}{x^3}=0\]
\[\frac{(x-3)(x^2+3x+9)}{x^3}=0\]
x=3

Answer 8

cjn, (2x)'=2 not x

Answer 9

yeah i saw that, thanks. disconnect between brain and keyboard.

Answer 10

any questions ry?

Answer 11

you need to check if the sign changes at 3 by pluggin in number before and after 3 to see if the sign does change

Answer 12

g''(1)=-
g''(4)=+
so yes the sign does change at x=3

Answer 13

I see.i put g'(x)=0 in mistake.Thanks anyway!!

Answer 14

? i thought you were looking for x
not g'?

Answer 15

i put g'(x)=0 instead of g''(x)=0
yea is finding x.

Answer 16

ok

Answer 17

thanks anyway:)