 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/10/b/solution

The two derivatives are

3 x^{2} + 3

and

6 x

, both equal to six at

x = 1

. Their common tangent line through

(1, 4)

y - 4 = 6 (x - 1)

, or

y = 6 x - 2

. Setting

x = 0

gives its intersection with the vertical axis:

(0, - 2) .

 New to topics? Read the docs here!