3.5.4 Differentiation (A-level only)

The cross-section of a custom aerodynamic fairing is modeled by a curve with equation

2y^2 + 3x = 4ye^{0.5x}

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

[4]

The curve intersects the $y$ -axis at the origin and at a point $P$ .

Find the equation of the normal to the curve at $P$ , writing your answer in the form $y = m x + c$ where $m$ and $c$ are constants to be found.

[4]

3.5.4 Differentiation (A-level only) Questions

The cross-section of a custom aerodynamic fairing is modeled by a curve with equation

2y^2 + 3x = 4ye^{0.5x}

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

[4]

The curve intersects the $y$ -axis at the origin and at a point $P$ .

Find the equation of the normal to the curve at $P$ , writing your answer in the form $y = m x + c$ where $m$ and $c$ are constants to be found.

[4]