Let f(x) = 3x2+2x+6. Two distinct lines l1 and l2 exist that are tangent to f(x) and intersect
at the origin. Given that l1 is tangent to f(x) at (x1; f(x1)) and that l2 is tangent to f(x) at
(x2; f(x2)), compute x1x2.	Choose the correct choice from the following answers.
A) -1  B) -2  C) -3  D) -4  E) -5
At any point (x0, y0) in f(x), the slope of the tangent line is   m = 6x0 + 2   Hence, the equation of the tangent line is given by   (y - y0) = m(x- x0)   y - (3x2   0 + 2x0 + 6) = (6x0 + 2)(x - x0)   y = (6x0 + 2)x - 6x2   0- 2x0 + 3x2   0 + 2x0 + 6   y = (6x0 + 2)x- 3x2   0 + 6   For the tangent line to cross the origin, we must have 3x2   0 - 6 = 0. This equation has two   solutions, the product of which is given by 􀀀6   3 = -2 .   correct answer -2
<result>B</result>
Let f(x) = 3x2+2x+6. Two distinct lines l1 and l2 exist that are tangent to f(x) and intersect
at the origin. Given that l1 is tangent to f(x) at (x1; f(x1)) and that l2 is tangent to f(x) at
(x2; f(x2)), compute x1x2.