Suppose that a kitchen appliance company\'s monthly sales and advertising expens

Question

Suppose that a kitchen appliance company's monthly sales and advertising expenses are approximately related by the equation xy-6x+20y=0, where x is thousands of dollars spent on advertising and y is the thousands of dishwasher sold. Currently, the company is spending 10 thousand dollars on advertising and is selling 2 thousand dishwashers each month. If the company plans to increase monthly advertising expenditures at the rate of $1.5 thousand per month, how fast will sales rise: Use implicit differentiation to answer the question.

Explanation / Answer

sol: Suppose a cubic crystal is growing so that the side changes at the rate of 10mm per second when the side length is 20 mm. If I want to know how fast the volume of the cube is growing at that time, I must use the equation V=x^3 and take the implicit derivative with respect to t and solve for dV/dt. or Suppose a plane is headed on a course of 050 at 300 mph and another is headed due north at 500 mph. If you want to know how fast the direct distance between them is changing, you must use implicit differentiation. In short, for everyday going to the grocery store type activities you won't need implicit differentiation. For complicated problems involving different rates of change you need to use implicit differentiation.

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