In online advertising, a common objective for advertisers is to get the maximum returns on investment given the budget. On one hand, if the bid is too high, the advertiser pays more money than he should pay for the same number of clicks. On the other hand, it the bid is too low, the advertiser cannot win in auctions and therefore it loses the opportunity. A challenging problem is how to recommend the bid to achieve the maximum values for advertisers. In this paper, we present an inflection point approach for bid recommendation from discovering the bid price of click(bid)1 function at which the function changes from significant increase (i.e. concave downward) to slow increase (convex upward). We derive the optimal solution using history sparse and noisy observations given the budget limit. In real word advertising campaign evaluations, the proposed bid recommendation scenario brings in 15.37% bid increase and 30.24% click increase over the baselines.