1. Verify the given formula by showing the left hand side of the equation simplifies to the right hand side of the equation. Difference of Cubes: (a-b) (a2+ab+b2) =a3-b3 2. Perform the indicated operations and simplify. 1 - 1 x+h x h 3. The daily cost, in dollars, to produce x Sasquatch Berry Pies C(x) = 3x + 36, x 0 and the price-demand function, in dollars per pie, is p(x) = 12 0.5x, 0 x 24. 4. Find the (implied) domain of the function. f(x) = 6x - 2 x2 - 36 5. The Topology Taxi Company charges $2.50 for the first fifth of a mile and $0.45 for each additional fifth of a mile. Find a linear function which models the taxi fare F as a function of the number of miles driven, m. Interpret the slope of the linear function and find and interpret F(0). 6. The height of an object dropped from the roof of an eight story building is modeled by: h(t) = 16t2 + 64, 0 < + < 2. Here, h is the height of the object off the ground in feet, t seconds after the object is dropped. Find and interpret the average rate of change of h over the interval [0, 2]. 7. What is the largest rectangular area one can enclose with 14 inches of string? 8. C(x) 11 on [2, 8]. This means anywhere between 2000 and 8000 pens can be produced and the cost will not exceed $1100