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Tangent Lines and the Physical Meaning of the Derivative

This test develops the geometric and physical interpretations of a derivative. Students form tangent equations, interpret velocity and acceleration and connect the sign of a derivative with the behaviour of a function.

Questions: 10Estimated time: 15 minutes
Tangent Lines and the Physical Meaning of the Derivative
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Sample questions

  1. For f(x) = ___x² + (___)x, find the tangent slope at x = ___.
  2. Find the tangent equation to f(x) = ___x² at x = ___.
  3. Position is s(t) = ___t² + (___)t. Find velocity at t = ___.
  4. Velocity is v(t) = ___t + (___). Find acceleration.
  5. What does a negative derivative of position mean at an instant?