I scanned the problem in, and the work that is underneath it, is what i tried to do.
Please help, Thanks!
Where did you take this question from? F(x) is a function of one variable so if THE tangent line at some point of the graph of F(x) exists then it is unique since its slope is given by the value of F'(x) at the x-coordinate of the tangency point. How can they ask something about "tangent lineS" at some point on the graph??
This must be a mistake or else this book's teaching stuff which I believe is not standard.
Tonio
maybe the question wants two distinct lines tangent to the curve that are perpendicular ... ?
if so, then given the symmetry of , one point of tangency would be and the other would be . note also that since is even,
and are opposite reciprocals ...
slopes ...
at , if and if
at , if and if
it should be obvious that the two tangent lines intersect on the y-axis
one of the tangent line equations is ...
for ...
the intersection point is
really ... a very poorly worded question.