Consider the curve $y = \frac{1}{{1 - x}} + \frac{4}{{x - 4}}$.

Find the x-coordinates of the points on the curve where the gradient is zero.

valid attempt to find $\frac{{{\text{d}}y}}{{{\text{d}}x}}$     M1

$\frac{{{\text{d}}y}}{{{\text{d}}x}} = \frac{1}{{{{\left( {1 - x} \right)}^2}}} - \frac{4}{{{{\left( {x - 4} \right)}^2}}}$      A1A1

attempt to solve $\frac{{{\text{d}}y}}{{{\text{d}}x}} = 0$     M1

$x = 2,\,\,x =  - 2$     A1A1

[6 marks]