 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-1/2/b/solution

Using the contact coordinate

x_{0} = 1

and substituting into the exponential function gives

(x_{0}, y_{0}) = (1, e) .

Both the curve and the line with the slope found in part (a) pass through this point.

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