Calculus I - Interpreting derivatives

3 flashcards · Mathematics · by luckydog789 (harrison holbrook)

1. Rated Rate problems

   Read the problem, making an illustration to properly organize the given information Identify the rates that are given and the rates to be determined Introduce rates of change by differentiating the appropriate equations(s) (with respect to time ttt ) Substitute known values and solve for the desired quantities Ensure that units are consistent and the answer is reasonable

2. Speed, velocity, acceleration, and jerk

   Suppose an object moves along a line with position s(t)s(t)s(t) The speed at time ttt is ∣s(t)∣|s(t)|∣s(t)∣ The velocity at time ttt is s′(t)s'(t)s′(t) The acceleration at time ttt is s′′(t)s''(t)s′′(t) The jerk at time ttt is s′′′(x)s'''(x)s′′′(x)

3. Average and marginal cost

   The cost function C(x)C(x)C(x) gives the cost to produce the first xxx items in a manufacturing process. The average cost to produce xxx items is C‾(x)=C(x)x\overline C(x) = \frac{C(x)}{x}C(x)=xC(x)​ The marginal cost C′(x)C'(x)C′(x) is the approximate cost to produce one additional item after producing x items