Complicated

[complicated]

I know I make things much more complicated that what they seem.

I am looking for help with a worksheet problem. I think I have the right answer, but I am not sure.

Find the largest open intervals where the function is concave upward.

f(x) = 6
x

I think it is = (0, ∞) can someone let me know if this is right before I turn it in? Thanks.

 

[pka]

Did you graph the expression?
Did you find where the the second derivative is positive?

 

[complicated]

No I didnt graph it. That is probably why I am confused.

 

[soroban]

Hello, complicated!

Find the largest open intervals where the function is concave upward.

\(\displaystyle f(x)\:=\:\L\frac{6}{x}\)

I think it is: \(\displaystyle \,(0,\,\infty)\)

You're right!

We have: \(\displaystyle \,f(x)\,=\,6x^{-1}\;\;\Rightarrow\;\;f'(x)\,=\,-6x^{-2}\;\;\Rightarrow\;\;f''(x)\,=\,12x^{-3}\)

For "concave upward", the second derivative must be positive.

\(\displaystyle \L\;\;\frac{12}{x^3}\) is positive if \(\displaystyle x\) is positive.

Your interval is correct.