1. Approximate E by using the tangent line approximation for f (x) = {5. Complete without a calculator. Show work and answer in fraction form (no decimals). Is this an over-approximation or under-approximation? Show how you know based on f \"(x). 2 2. Show all of your work to support your answer: If f (6) = 30 and f ' (x) = xx: , then an estimate of f (6.02) using the tangent line is . . . (A) 29.92 (B) 30.02 (C) 30.03 (D) 34.00 (E) None of These 3. Find the absolute extrema for y = e" sinx on [0,}: ]. Provide both x and y. Make sure you specify which points are maximums and which are minimums. Don't put answers in decimal form; do not use a calculator. 2 4. Find the absolute extrema for f (x) = x on [-1, 1X2]. Provide both x and f(x). Make sure you specify xl which points are maximums and which are minimums. Explain why the Extreme Value Theorem applies to this function over this interval. 5. Find two positive numbers in which the sum of the rst and twice the second is 100, and the product is a maximum. Show how you know the solution is a maximum rather than a minimum. 6. An open box is to be made from a 3-foot by 5-foot rectangular piece of material by cutting equal squares from each comer and turning up the sides. Find the volume of the largest box that can be made in this manner. One critical value will the thrown out. Show it and explain why. 7. A farmer plans to fence a rectangular pasture for his cows. He is placing the pasture next to a river so that they can drink water. He doesn't fence the side next to the river. The pasture must contain 500,000 square meters. What dimensions would require the least amount of fencing for the 3 sides of the fence