1.9.16 Implicit differentiation (A-level only)

A cross-section of a micro-fluidic channel is modeled by the curve with equation

3x^2y - bx^3 + \frac{1}{2}y^2 = 4

where $b$ is a positive constant.

a.

Show that

\frac{dy}{dx} = \frac{3x(bx - 2y)}{3x^2 + y}

[4]

b.

Given that the curve has a stationary point at $x = 1$ , determine the value of $b$ .

[4]

A cross-section of a micro-fluidic channel is modeled by the curve with equation

3x^2y - bx^3 + \frac{1}{2}y^2 = 4

where $b$ is a positive constant.

a.

Show that

\frac{dy}{dx} = \frac{3x(bx - 2y)}{3x^2 + y}

[4]

b.

Given that the curve has a stationary point at $x = 1$ , determine the value of $b$ .

[4]

1.9.16 Implicit differentiation (A-level only) Questions