 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/11/a/solution

If tangency occurs at

x_{*}

, the slope must satisfy both

k = 2 e^{2 x_{*}}

and

k x_{*} = e^{2 x_{*}}

. Eliminating

k

gives

2 x_{*} = 1

k = 2 e .

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