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

What these 13 flashcards ask

What does f''(x)0 tell you about a curve?
What does f''(x)<0 tell you about a curve?
Define a point of inflection.
Is f''(x)=0 alone enough for an inflection?
Is a point of inflection always stationary?
What is a stationary point of inflection?
What is the origin on y=x^{4}?
What is the origin on y=x^{3}?
What if f'(x)=0 and f''(x)=0?
Which derivative decides increasing/decreasing?
Which derivative decides convex/concave?
Where on an N-t curve is the rate of growth greatest?
Steps to find a point of inflection?

Exam questions on Convex and concave curves and points of inflection

The curve $C$ has equation $y=x^{3}-6x^{2}+2$ .
Find the coordinates of the point of inflection of $C$ , justifying that it is a point of inflection.2 marks
Let $f(x)=x^{4}$ and $g(x)=x^{3}$ . For both functions, the first and second derivatives are equal to $0$ at $x=0$ .
Explain why $f''(0)=0$ is not enough to show that the origin is a point of inflection on $y=f(x)$ .2 marks
A curve has equation $y=x^{4}-8x^{3}+18x^{2}$ .
Find the coordinates of the points of inflection of the curve, justifying your answer.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).