Stationary points and increasing and decreasing functionsAQA A-Level Maths: Mind map

Exam questions on Stationary points and increasing and decreasing functions

1. The curve $C$ has equation $y=x^3-6x^2+9x+2$.
   Find the set of values of $x$ for which $y$ is decreasing.2 marks
2. The curve $C$ has equation $y=x+\frac{16}{x}$ for $x>0$.
   Find the minimum value of $y$, justifying that it is a minimum.2 marks
3. An open-topped box has a square base of side $x$ cm and height $h$ cm. It is made from $300$ cm$^2$ of card, so the base and four sides use all of the card. The volume of the box is $V$ cm$^3$.
   Show that $V=75x-\frac{x^3}{4}$.3 marks