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Derivatives as rates of change worksheets Grade 12

Use derivatives to find velocity and other rates of change.

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How to do it

The derivative is the rate of change: velocity is the derivative of position.

s(t)=2t3−2t2−8t+7 is a position. Velocity at t=4→72s(t) = 2t^{3} - 2t^{2} - 8t + 7\ \text{is a position. Velocity at }t = 4\quad \to \quad 72
v(t)=s′(t)=6t2−4t−8v(t) = s'(t) = 6t^{2} - 4t - 8velocity is the derivative of position
v(4)=6(4)2−4(4)−8=72v(4) = 6(4)^{2} - 4(4) - 8 = 72

Example problems

  1. s(t)=t3+9t2+7t−5 is a position. Velocity at t=5→s(t) = t^{3} + 9t^{2} + 7t - 5\ \text{is a position. Velocity at }t = 5\quad \to \quad
  2. s(t)=3t3−2t2+5 is a position. Velocity at t=2→s(t) = 3t^{3} - 2t^{2} + 5\ \text{is a position. Velocity at }t = 2\quad \to \quad
  3. s(t)=−2t3+5t2+2t+7 is a position. Velocity at t=2→s(t) = -2t^{3} + 5t^{2} + 2t + 7\ \text{is a position. Velocity at }t = 2\quad \to \quad
  4. s(t)=3t3−5t2+3t−3 is a position. Velocity at t=2→s(t) = 3t^{3} - 5t^{2} + 3t - 3\ \text{is a position. Velocity at }t = 2\quad \to \quad

Limits and derivatives

  1. Evaluating limits
  2. The power rule for derivatives
  3. The product rule
  4. The quotient rule
  5. The chain rule
  6. Derivatives of trig, exponential and log functions
  7. Equation of a tangent line
  8. Derivatives as rates of change
  9. Finding maximum and minimum points