Find the equation of the normal to the curve $y = \frac{{{{\text{e}}^x}\cos x\ln (x + {\text{e}})}}{{{{({x^{17}} + 1)}^5}}}$ at the point where $x = 0$.

In your answer give the value of the gradient, of the normal, to three decimal places.

$x = 0 \Rightarrow y = 1$     (A1)

$y'(0) = 1.367879 \ldots$     (M1)(A1)

Note:     The exact answer is $y'(0) = \frac{{{\text{e}} + 1}}{{\text{e}}} = 1 + \frac{1}{{\text{e}}}$.

so gradient of normal is $\frac{{ - 1}}{{1.367879 \ldots }}\;\;\;( =  - 0.731058 \ldots )$     (M1)(A1)

equation of normal is $y =  - 0.731058 \ldots x + c$     (M1)

gives $y =  - 0.731x + 1$     A1

Note:     The exact answer is $y =  - \frac{{\text{e}}}{{{\text{e}} + 1}}x + 1$.

Accept $y - 1 =  - 0.731058 \ldots (x - 0)$

[7 marks]

Surprisingly many candidates ignored that fact that paper 2 is a calculator paper, attempted an algebraic approach and wasted lots of time. Candidates that used the GDC were in general successful and achieved 7/7. A number of candidates either found the equation of the tangent or used the positive reciprocal for the normal and many did not find the value of $y$ corresponding to $f(0)$.