1. Find a function f(x) such that f'(x) = -2x2 - 7 and f(0) = 2.
2. A company has found that the cost, in dollars per pound, of the coffee it roasts is related to C'(x) = -0.016x + 8.75, for x ≤ 300, where x is the number of pounds of coffee roasted. Find the total cost of roasting 150 lb of coffee.
3. The amount of trash, in tons per, produced by a town has been growing linearly, and is projected to continue growing according to the formula P(t) = 65 + 2t. Estimate the total trash that will be produced over the next 6 years by interpreting the integral as an area under the curve.