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1.10.5 Implicit and parametric differentiation (A-level only)

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Question 24

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+21​y2=4

where bbb is a positive constant.

a.

Show that

dydx=3x(bx−2y)3x2+y \frac{dy}{dx} = \frac{3x(bx - 2y)}{3x^2 + y} dxdy​=3x2+y3x(bx−2y)​
[4]
b.

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

[4]

1.10.5 Implicit and parametric differentiation (A-level only) Questions

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