Solve these question using Derivatives
1. A spotlight on the ground shines on a wall 12 meters away. If a man 2 meters tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?
2. Find the dimensions of a rectangle with area of 1000 m3 whose perimeter is as small as possible.
3. A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material of the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of the materials for the cheapest such container.
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