# Thread: find derivative then solve for x

1. ## find derivative then solve for x

f(x)= (x^3)lnx

f'(x) = (3x^2)(lnx) +(x^3)(1/x)
= (3x^2)lnx + x^2
= x^2(3lnx+1)

x^2 = 0
x=0

3lnx +1 =0
lnx =-1/3

x=e^(-1/3)

is my work all correct?

I was able to find find f''(x) of x^2(3lnx+1) so I don't know.

2. ## Re: find derivative then solve for x

What is your ultimate goal with this problem? What are you trying to determine?

3. ## Re: find derivative then solve for x

I am trying to find out where f interval increase and decrease.

so far I have

INCREASE: ( __ , infinity)

DECREASE: ( 0, __ )

4. ## Re: find derivative then solve for x

Originally Posted by NeoSonata
f(x)= (x^3)lnx

f'(x) = (3x^2)(lnx) +(x^3)(1/x)
= (3x^2)lnx + x^2
= x^2(3lnx+1)

x^2 = 0
x=0

3lnx +1 =0
lnx =-1/3

x=e^(-1/3)

is my work all correct?
Yeh, this looks good, now graph the function using technology, is $\displystyle \frac{1}{\sqrt[3]{e}}\approx 0.72$ in the neighbourhood of your turning point?

5. ## Re: find derivative then solve for x

yeah..

___________________
0 ---- .72 ++++++

so it should be increasing from (.72, infinity) and decreasing from (0, .72) ?

web-assign will not accept so probably the system is incorrect.

6. ## Re: find derivative then solve for x

Originally Posted by NeoSonata

so it should be increasing from (.72, infinity) and decreasing from (0, .72) ?
That's how I see it.

7. ## Re: find derivative then solve for x

Maybe WebAssign needs more digits for accuracy, or maybe it needs the exact result.

8. ## Re: find derivative then solve for x

It might do, I'm not aware of this software.

If you were doing a written exam the exact value of e^(-1/3) will always be best.