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]