Setting the derivative 0 and solving did I get the right results?

[Femme_physics]

The function and my attempt to find the critical points by setting the derivative equal to zero are in the attachment. Is this correct?

 

[I like Serena]

You have f'(x)=2x-16x^-2.

Could you try calculating f'(2) and more specifically f'(8)?
If your solution is correct they should both be zero.

 

[Femme_physics]

*smacks forehead*

Good idea! So 8 is definitely wrong, 2 is correct. Is 2 the only correct answer then?

 

[I like Serena]

*smacks forehead*

Good idea! So 8 is definitely wrong, 2 is correct. Is 2 the only correct answer then?

Yes.

In general x³=a has 1 real solution (and 2 imaginary ones).
The real solution is x=a^1/3.

 

[Femme_physics]

I'll remember that. :) Much appreciated Serena...you're the best.

 

[gb7nash]

Also, don't forget about x = 0, where the derivative is not defined.