Chapter 6: Further applications of calculus Notes

Sections

1. 6A Sketching polynomials from their zeroes Mastered

   Reviewing the factor theorem, sketching a polynomial from its linear factors, the behaviour of the graph at zeroes of odd and even multiplicity, and the leading term at the far left and right.

   Open notes
2. 6B Multiple zeroes and the derivative Mastered

   A zero of multiplicity m of a polynomial is a zero of multiplicity m − 1 of its derivative, testing for double zeroes with P(α) = P'(α) = 0, and finding unknown coefficients from a multiple zero.

   Open notes
3. 6C Related rates Mastered

   Using the chain rule to link rates of change of related quantities, such as an inflating balloon, a filling conical tank and an expanding ripple, and the steps for solving related rates problems.

   Open notes
4. 6D Modified exponential growth Mastered

   The modified exponential model dN/dt = k(N − P) and its solution N = P + Ae^{kt}, Newton's law of cooling, finding constants from data, limiting values, and solving for times using logarithms.

   Open notes
5. 6E Volumes of revolution Mastered

   Volumes of solids formed by rotating a region about the x-axis or the y-axis, the formulas V = π∫y²dx and V = π∫x²dy, the volumes of a cone and a sphere, and the volume between two curves.

   Open notes