The function $f$ is defined by

$f(x)=2{x}^{3}+p{x}^{2}+3x-16$

where $p$ is a constant.

Find all the possible values of $p$ for which the equation

$f'(x)=0$

has at least one real solution.

A curve has equation

$y=\frac{1}{{x}^{5}}({x}^{2}+\sqrt{x}-1)$

Find $\frac{dy}{dx}$.

This question has 2 part(s).

A curve has equation

$y={(\frac{1}{x}-\frac{1}{x\sqrt{x}})}^{2}x>0$

Find $\frac{dy}{dx}$, writing your answer in the form

$\frac{dy}{dx}=a{x}^{{k}_{1}}+b{x}^{{k}_{2}}+c{x}^{{k}_{3}}$

where

• $a$, $b$ and $c$ are constants to be found

• ${k}_{1}$, ${k}_{2}$ and ${k}_{3}$ are terms of a descending arithmetic sequence to be found