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1.7.19 Parametric and implicit differentiation (A-level only)

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Question 54

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

The cross-section of a high-tensile structural support beam is modeled by the curve defined by the equation

3y2−4xy+2x2+6x=20 3y^2 - 4xy + 2x^2 + 6x = 20 3y2−4xy+2x2+6x=20

where xxx and yyy are coordinates in decimetres. The boundary of the cross-section intersects the positive xxx-axis at the point RRR.

a.

State the coordinates of RRR.

[2]
b.

The curve has two stationary points, PPP and QQQ, where the tangent to the curve is horizontal.

Show that, at points PPP and QQQ,

ax2+bx+c=0 ax^2 + bx + c = 0 ax2+bx+c=0

where aaa, bbb and ccc are integers to be found.

[5]
c.

Find the xxx-coordinate of point QQQ, given that xQ>0x_Q > 0xQ​>0, giving your answer to 3 decimal places.

[2]

1.7.19 Parametric and implicit differentiation (A-level only) Questions

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