Application of Differentiation · CAPE Integrated Mathematics

7 past-paper questions on Application of Differentiation, part of Calculus, from every CAPE Integrated Mathematics paper on Quelpr.

1. 5(c)(i)3 marks· CAPE Integrated Mathematics · 2016 · Paper 2Find the second derivative, P''(t).
2. 5(c)(ii)2 marks· CAPE Integrated Mathematics · 2016 · Paper 2Given that the function P(t) has a stationary point when t = 48, show that the stationary point is a maximum point.
3. 5(c)(iii)3 marks· CAPE Integrated Mathematics · 2016 · Paper 2Find the population count when t = 48 days.
4. 5(d)(i)1 mark· CAPE Integrated Mathematics · 2016 · Paper 2Obtain an expression for dV/dt.
5. 5(d)(ii)4 marks· CAPE Integrated Mathematics · 2016 · Paper 2Find the rate of increase of the volume of the balloon, dV/dt, at the instant when r = 5 cm. Give your answer in terms of pi.
6. 5(d)4 marks· CAPE Integrated Mathematics · 2017 · Paper 2If Z(x, y) = x^3 + 4y^2 + \ln y, calculate the partial derivative \frac{\partial Z}{\partial y}.
7. 5(e)3 marks· CAPE Integrated Mathematics · 2017 · Paper 2A small business profit function (in dollars) for a year is given by P(x) = 150x - \frac{9}{20}x^2 - 1500, where x represents the number of cakes sold. Estimate the number of cakes that must be sold to get the maximum…