A curve has equation $y = x^3 - 48x$ - AQA - A-Level Maths Mechanics - Question 15 - 2018 - Paper 1

To show that point A is a stationary point, we need to analyze the gradient found in part (a).

As $h \to 0$, the gradient of the line AB, which is given by $h^2 - 12h$, approaches:

$\lim_{h \to 0}(h^2 - 12h) = 0.$

Since the gradient of the curve at point A is the same as the gradient of line AB, we conclude that the gradient approaches zero at point A. Thus, A must be a stationary point on the curve.