Array with a mountain shape

Given an array in which initially elements start increasing till some index k and then they decrease. Find k.

Of course this asks us to find k in sub linear time. Otherwise, the most obvious solution is to check every element till elements increase and then at first drop in value, you get k. Sub linear acts as a hint for logarithmic. Logarithmic gives hint for dividing and throwing away some part, so that we reach a singleton or small enough set quickly. Let's see whether we can discard some part of the array. What if we pick the middle as we do in binary search? This gives us m=(i+j)/2 and m<=k or m>k. If we can somehow establish this relation between m and k (note: k is unknown, we have to find it), we can throw away the remaining part. How can we do this then? We know that k is the index such that on its left, the line plot of the array is ascending and on its right, it is descending. This means, if we are on left of k, we are on upward slope as against when we are on the right part of k. This hint is enough I guess. Once we get m, check a[m-1], a[m] and a[m+1] to get an indication about the region of slope where m belongs to, by comparison. Once we know that we are on upward slope, we know that m<=k, so we discard this part. Similarly for the case when m>k. Once we reduce problem size from n to n/2 at every iteration, we are in logarithmic space. Thus the algorithm performs in O(log n).