A specialist optical lens has a cross-section defined by the curve $C$ . The coordinates $(x, y)$ , measured in millimeters, of the surface of the lens satisfy the equation

x^2 y + 10y = 2x^3 - 15x^2 + k, \quad y > 0

where $k$ is a constant.

Find $dydx\dfrac{dy}{dx}$ in terms of $x$ and $y$ .

The point $P (p, 3)$ , where $p$ is a constant, lies on $C$ . Given that $P$ is the minimum turning point on $C$ ,

find

(i) the value of $p$

(ii) the value of $k$

A specialist optical lens has a cross-section defined by the curve $C$ . The coordinates $(x, y)$ , measured in millimeters, of the surface of the lens satisfy the equation

x^2 y + 10y = 2x^3 - 15x^2 + k, \quad y > 0

where $k$ is a constant.

Find $dydx\dfrac{dy}{dx}$ in terms of $x$ and $y$ .

The point $P (p, 3)$ , where $p$ is a constant, lies on $C$ . Given that $P$ is the minimum turning point on $C$ ,

find

(i) the value of $p$

(ii) the value of $k$

Differentiation

Question 566

Markscheme

Differentiation

Question 566

Markscheme

Differentiation

Question 566

Differentiation Questions

Differentiation

Question 566

Differentiation Questions