A cross-section of a micro-fluidic channel is modeled by the curve with equation
3x2y−bx3+12y2=4 3x^2y - bx^3 + \frac{1}{2}y^2 = 4 3x2y−bx3+21y2=4where bbb is a positive constant.
Show that
dydx=3x(bx−2y)3x2+y \frac{dy}{dx} = \frac{3x(bx - 2y)}{3x^2 + y} dxdy=3x2+y3x(bx−2y)Given that the curve has a stationary point at x=1x = 1x=1, determine the value of bbb.
82 exam-style questions on CCEA A Level Maths 3.5.4 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.