 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-1/section-a/6/solution

x = 1

permits

t = 0

t = - 2

, but only

t = 0

also gives

y = 0

. The chain rule gives the slope

\frac{d y}{d x} = \frac{d y / d t}{d x / d t} = \frac{12 - 3 t ^{2}}{2 ( 1 + t )} .

At the required point,

t = 0

, so

\frac{d y}{d x} = 6.

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