A curve, representing the vertical cross-section of a high-precision optical lens, has the equation y=2x3−96xy = 2x^3 - 96xy=2x3−96x.
The point PPP on the curve has xxx-coordinate 444.
The point QQQ on the curve has xxx-coordinate 4+h4 + h4+h.
Show that the gradient of the chord PQPQPQ is 2h2+24h2h^2 + 24h2h2+24h.
Explain how the result of part (a) can be used to show that PPP is a stationary point on the curve.
