Stationary points and increasing and decreasing functionsAQA A-Level Maths: Flashcards

What these 12 flashcards ask

What is a stationary point?
When is a function increasing?
When is a function decreasing?
How do you find the y-coordinate of a stationary point?
What does \frac{d^2y}{dx^2} measure?
What does \frac{d^2y}{dx^2}0 at a stationary point show?
What does \frac{d^2y}{dx^2}<0 at a stationary point show?
What if \frac{d^2y}{dx^2}=0 at a stationary point?
Gradient test for a local maximum?
Gradient test for a local minimum?
Stationary points of y=x^3-6x^2+9x+2?
Steps in an optimisation problem?

Exam questions on Stationary points and increasing and decreasing functions

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).