The curve $C$ has equation $y=\frac{3{{x}^{2}}-px-1}{x-p}$ where $p$ is a constant. If $C$ has no st

Question

The curve $C$ has equation $y=\frac{3{{x}^{2}}-px-1}{x-p}$ where $p$ is a constant. If $C$ has no stationary points, use an alegbraic method to find the range of possible values of $p$. [4] It is given that the equation of the oblique asymptote of $C$ is $y=3x-1$. Find the value of $p$. [1] For the rest of the question, use the value of $p$ found in part (ii). Sketch the curve $C$, stating clearly the equations of the asymptotes and the coordinates of any stationary point(s) and the coordinates of any axial intercept(s). [3] By sketching another suitable curve on the same diagram in part (iii), deduce the number of real roots of the equation $3{{x}^{3}}-p{{x}^{2}}-x=2x-2p$. [3]

Accepted Answer

$-\dfrac{1}{\sqrt{2}} < p < \dfrac{1}{\sqrt{2}}$; $p = -\dfrac{1}{2}$; 3 real roots

2022 CJC J1 MYE Q9

2022 CJC J1 MYE Q9

Video Solution:

Solution:

Solution locked