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

Femme_physics · Apr 20, 2011

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 · Apr 20, 2011

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 · Apr 20, 2011

*smacks forehead*

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

I like Serena · Apr 20, 2011

Femme_physics said:

*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 · Apr 20, 2011

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

gb7nash · Apr 20, 2011

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

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