How to tell if f(x) = x2-1-1/x is concave up or down?

[Strat]

I'm trying to see if this is concave up or down:

f(x) = x²-1-1/x

I've found the second derivative:
f''(x): -2x²-1

And solved for x, which gets me sqrt(-1/2) = x

This seems impossible since i would be in the answer. I've treated it as +or- 1/2 = x and then tried plugging those numbers back into the f''(x) but I get all negative answers, which would mean the graph is concave down, but the answer is concave up from 0 to infinity. Where am I going wrong?

 

[Deleted member 4993]

I'm trying to see if this is concave up or down:

f(x) = x²-1-1/x

I've found the second derivative:
f''(x): -2x²-1

And solved for x, which gets me sqrt(-1/2) = x

This seems impossible since i would be in the answer. I've treated it as +or- 1/2 = x and then tried plugging those numbers back into the f''(x) but I get all negative answers, which would mean the graph is concave down, but the answer is concave up from 0 to infinity. Where am I going wrong?

Is:
\(\displaystyle \displaystyle{f(x) \ = \ x^2 \ - \ 1 \ - \ \dfrac{1}{x}} \ . \ . \ . \)?

then f"(x) is NOT -2x² - 1

 

[Strat]

Is:
\(\displaystyle \displaystyle{f(x) \ = \ x^2 \ - \ 1 \ - \ \dfrac{1}{x}} \ . \ . \ . \)?

then f"(x) is NOT -2x² - 1

Yes that is what I meant. I found the derivative twice and got the same answer each time...

 

[Deleted member 4993]

Is:
\(\displaystyle \displaystyle{f(x) \ = \ x^2 \ - \ 1 \ - \ \dfrac{1}{x}} \ . \ . \ . \)?

\(\displaystyle \displaystyle{f(x) \ = \ x^2 \ - \ 1 \ - \ \dfrac{1}{x}} \ . \ . \ . \)

\(\displaystyle \displaystyle{f'(x) \ = \ 2x \ + \ \dfrac{1}{x^2}} \ . \ . \ . \)

\(\displaystyle \displaystyle{f"(x) \ = \ 2 \ - \ \dfrac{2}{x^3}} \ . \ . \ . \)

You should get this for f"(x)

 

[stapel]

Yes that is what I meant. I found the derivative twice and got the same answer each time...

Please reply showing your work, so we can see how you're getting that the derivative of x^(-1) is zero. Thank you!