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Warm-Up Question

Warm-Up Question. For each equation, find implicitly. Applications of Derivatives. Related Rate. Related Rate Problems. Lesson : P. 180.

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Warm-Up Question

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  1. Warm-Up Question For each equation, find implicitly.

  2. Applications of Derivatives Related Rate

  3. Related Rate Problems Lesson:P. 180 If Q is a quantity that varies with time, then the derivative of Q respect to time t, namely dQ/dt gives the rate of change of that quantity with respect to time. In order to find dQ/dt where Q is a quantity expressed with other variables such as length, width, radius, and weight, we use the implicit differentiation technique. Example: P. 181 1) A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, at what rate is the volume increasing when the radius is 5 inches? Required Practice: P.185 7

  4. More Related Rate Problems (1/3) Example:P. 181 An object is moving in the clockwise direction around the unit circle . As it passes through the point , its y-coordinate is decreasing at the rate of 3 units per second. At what rate is the x-coordinate changing at this point? Required Practice: P.185 1, 3 Additional Practice: P.185 5

  5. More Related Rate Problems (2/3) Example:P. 182 A ladder 13 feet long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at the rate of 0.1 foot per second, how fast is the angle formed by the ladder and the ground changing at the instant when the top of the ladder is 12 feet above the ground? Required Practice: P.185 17, 9 Additional Practice: P.185 10

  6. More Related Rate Problems (3/3) Example:P. 182 Two ships, one heading west and the other east, approach each other on parallel courses 8 nautical miles apart. Given that each ship is cruising at 20 nautical miles per hour (knots), at what rate is the distance between them diminishing when they are 10 nautical miles apart? Required Practice: P.185 15

  7. Homework P. 185 2, 8, 14, 18

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