Problem : Find the derivative of f (x) = 3x4 -2x2 +5x-1 and evaluate it at x = 2.Using the basic calculus rules established in this section, we find that
Problem : Find the velocity and acceleration functions corresponding to the position function x(t) = 3t2 - 8t + 458.v(t) = x'(t) and a(t) = v'(t) = x''(t), so using our basic calculus rules again we find that
Problem : What happens when a car which is traveling along at constant velocity screeches to a halt?The velocity of the car decreases rapidly, corresponding to a large negative acceleration (or deceleration) of the vehicle (courtesy of good brakes). While the car was traveling at constant velocity, on the other hand, the acceleration was zero.
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