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1. Find the critical point(s) and determine the nature of the critical point(s) of the curve y = 3×4-4×3 +5.

2. A firm produces a good from a raw material that costs 2 dollar per unit. Using 2r units of raw material, the firm can produce (2r) units of its good, where a is a fixed number such that 0 < a < 1. The selling price of the good is 1 dollar per unit. Show that the maximum profit the firm can achieve is
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