Convex and concave curves and points of inflectionAQA A-Level Maths: Flashcards

What these 12 flashcards ask

What does it mean for a curve to be convex?
What does it mean for a curve to be concave?
What is a point of inflection?
What two conditions identify a point of inflection?
Does \frac{d^2y}{dx^2}=0 always give a point of inflection?
How do you find the y-coordinate of a point of inflection?
Point of inflection of y=x^3?
Can a point of inflection have non-zero gradient?
What does \frac{d^2y}{dx^2} represent?
How do you test the regions between roots of \frac{d^2y}{dx^2}?
Where is the gradient of a cubic least or greatest?
If a cubic has an inflection at x=1, how do you find an unknown constant?

Exam questions on Convex and concave curves and points of inflection

The curve $C$ has equation $y=x^3-6x^2+5x$ .
Find the equation of the tangent to $C$ at its point of inflection.2 marks
The curve $C$ has equation $y=x^4-4x^3+6$ .
Find the coordinates of both points of inflection of $C$ .2 marks
The curve $C$ has equation $y=x^2+\frac{8}{x}$ for $x\neq0$ .
Show that $C$ has exactly one point of inflection and find its coordinates.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).