1.9.16 Implicit differentiation (A-level only)

The flight path of a search-and-rescue drone following a specific signal intensity contour is modeled by the equation

x^2 + 2y^3 - 12xy = 0

for $\ge 0$ . The path has a stationary point at $P$ in the first quadrant where the tangent to the path is horizontal.

Show that the $y$ -coordinate of $P$ satisfies the equation

y^2(y - 18) = 0

[6]

Hence, determine the coordinates of $P$ .

[3]

1.9.16 Implicit differentiation (A-level only) Questions

The flight path of a search-and-rescue drone following a specific signal intensity contour is modeled by the equation

x^2 + 2y^3 - 12xy = 0

for $\ge 0$ . The path has a stationary point at $P$ in the first quadrant where the tangent to the path is horizontal.

Show that the $y$ -coordinate of $P$ satisfies the equation

y^2(y - 18) = 0

[6]

Hence, determine the coordinates of $P$ .

[3]