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

Exam questions on Convex and concave curves and points of inflection

1. 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
2. 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
3. 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