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Practice Problems for 4/15

  1. Let \(x\) and \(y\) represent two non-negative numbers whose sum is 9. Find \(x\) and \(y\) so that the product of one number and the square of the other is maximized.

  2. Find the function \(f(x)\) whose derivative is \(f'(x)=x^2-4\) and \(f(3)=-5\).

  3. An impatient driver wants to pass the car in front of him. What constant acceleration, \(a\), is required to increase the speed of the passing car from 30 mph to 50 mph in 5 seconds?