A cylinder has a radius r r\,r and a height hhh.
The surface area of the cylinder is 500cm2
Show that the volume (V cm3V \text{ cm}^3V cm3) of the cylinder is given by V=250r−πr3V = 250r - \pi r^3V=250r−πr3
Calculate the maximum value of VVV, to the nearest cm3\text{cm}^3cm3
Justify that the value of V V\,V you found is a maximum.
28 exam-style questions on Edexcel AS Level Maths Differentiation, covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.