3.6.6 Differentiation (A-level only)

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

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

where $x$ and $y$ are coordinates in decimetres. The boundary of the cross-section intersects the positive $x$ -axis at the point $R$ .

State the coordinates of $R$ .

[2]

The curve has two stationary points, $P$ and $Q$ , where the tangent to the curve is horizontal.

Show that, at points $P$ and $Q$ ,

ax^2 + bx + c = 0

where $a$ , $b$ and $c$ are integers to be found.

[5]

Find the $x$ -coordinate of point $Q$ , given that $x_Q > 0$ , giving your answer to 3 decimal places.

[2]

3.6.6 Differentiation (A-level only) Questions