The trajectory of a specialized particle in a particle accelerator is modeled by the curve $C\,$ with equation

e^{-4y}, \quad y \in \mathbb{R}

Show that, for points on $C\,$ with $y≠0,14\displaystyle y\ne 0,\frac14$ ,

\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{y}{x(1 - 4y)}

and state separately the value of $dydx\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}$ at the origin $(0, 0)$ .

Given that a vertical detector strip at $x = k$ , where $k\,$ is a constant, detects the particle at exactly two distinct locations on the curve $C$ ,

find the range of possible values for $k$ .

The trajectory of a specialized particle in a particle accelerator is modeled by the curve $C\,$ with equation

e^{-4y}, \quad y \in \mathbb{R}

Show that, for points on $C\,$ with $y≠0,14\displaystyle y\ne 0,\frac14$ ,

\frac{\mathrm{d} y}{\mathrm{d} x} = \frac{y}{x(1 - 4y)}

and state separately the value of $dydx\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}$ at the origin $(0, 0)$ .

Given that a vertical detector strip at $x = k$ , where $k\,$ is a constant, detects the particle at exactly two distinct locations on the curve $C$ ,

find the range of possible values for $k$ .

Differentiation

Question 107

Markscheme

Differentiation

Question 107

Markscheme

Differentiation

Question 107

Differentiation Questions

Differentiation

Question 107

Differentiation Questions