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Second derivative question

Attached is a photo of the question. I have calculated the second derivative but I'm unsure how to show that the curvature d2q/dk2 is negative for k < k1 and is positive for k > k1. At this point I need to find the value of k1.

Any ideas? Thanks for the help!

Attachment 29639

Re: Second derivative question

I can't read your attachment

Re: Second derivative question

Set it equal to zero. That will allow you to calculate $\displaystyle k_1$. Then, plug in a value to the left of $\displaystyle k_1$ and to the right of $\displaystyle k_1$. You will find the second derivative is zero when $\displaystyle k = 2k_m$. If $\displaystyle k<2k_m$, the second derivative will be negative. If $\displaystyle k>2k_m$, the second derivative will be positive.