The diagram below shows part of the graph of the function $f(x) = e^{-x^2}$, where $x \geq 0$. [DI...
The graph of the function $y = \dfrac{xe^{3x}}{2x + k}$, where $k$ is a non-zero constant, has a sin...
Show that $y = \sin(x^2) - \cos(x)$ is a solution to the equation $\dfrac{d^2y}{dx^2} + 4x^2\,y = 2...
Find the $x$-value(s) of any stationary points on the graph of the function below, and determine the...
A curve is defined by the equation $y = \dfrac{2x^2 - 1 - 2x \ln x}{x}$ , where $x > 0$. The curve...