3.6.6 Differentiation (A-level only)

A robotic welding tool follows a path in the $x y$ -plane described by the implicit equation

3y^2 - 12y = 4x^2 + 16x - 16

Determine an expression for $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[3]

The path of the tool is discontinuous, and it cannot operate within an exclusion zone defined by the $x$ -interval $(p, q)$ .

By considering the points on the curve where the tangent is vertical, find the exact values of $p$ and $q$ .

[5]

3.6.6 Differentiation (A-level only) Questions

A robotic welding tool follows a path in the $x y$ -plane described by the implicit equation

3y^2 - 12y = 4x^2 + 16x - 16

Determine an expression for $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[3]

The path of the tool is discontinuous, and it cannot operate within an exclusion zone defined by the $x$ -interval $(p, q)$ .

By considering the points on the curve where the tangent is vertical, find the exact values of $p$ and $q$ .

[5]