Stationary points and increasing and decreasing functionsEdexcel International A Level Maths: Mind map

Exam questions on Stationary points and increasing and decreasing functions

1. The curve $C$ has equation $y=x^3-6x^2+9x+2$.
   Find the $y$-coordinates of the two stationary points of $C$.2 marks
2. The function $\mathrm{f}$ is defined by $\mathrm{f}(x)=2x^3-3x^2-12x+5$.
   Hence find the range of values of $k$ for which the equation $\mathrm{f}(x)=k$ has three distinct real roots.2 marks
3. The curve $C$ has equation $y=x+\frac{4}{x^2}$, for $x>0$.
   Find $\frac{dy}{dx}$ and hence find the coordinates of the stationary point of $C$.3 marks