This post includes eight questions.

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  1. Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x) = x^2 – 10x – 7; [4,7]
  2. The total profit P(x) (in thousands of dollars) from the sale of x hundred thousand pillows is approximated by: P(x) = -x^3 + 12x^2 + 99x – 200, x ≥ 5. Find the number of hundred thousands of pillows that must be sold to maximize profit. Find the maximum profit.
  3. A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With 700m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?
  4. A fence must be built to enclose a rectangular area of 45000 ft^2. Fencing material costs $1 per foot for the two sides facing north and south, and $2 per foot for the other two sides. Find the cost of the least expensive fence.
  5. A rectangular box with a volume of 1280 ft^3 is to be constructed with a square base and top. The cost per square foot for the bottom is 15(cents), for the top is 10(cents), and for the sides is 1.5(cents). What dimensions will minimize the cost?
  6. Find (dy)/(dx) using implicit differentiation. 5x^3 = 7y^2 – 3y
  7. Suppose that x and y are related by the given equation and use implicit differentiation to determine (dy)/(dx). x^7y + y^7x = 4
  8. Find the equation of the tangent line at the given value of x on the curve. 2y^3 + xy – y = 54x^4; x=1

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