Specialist2025 Exam 2 Section A · Q2CAS active1 mark

Counter-example for point of inflection

Consider the following statement.

'If $f''(0) = 0$ , then the graph of $f$ necessarily has a point of inflection at $x = 0$ .'

A counter-example that disproves this statement is when

1 mark

f(x) = \sin^{-1}(x)

f(x) = \dfrac{2x}{x^2 - 1}

f(x) = x^{\frac{1}{3}}

f(x) = x^4 - x

Hints, answer checking and worked solutions come with a Season Pass.