F(x) = kx^2 + 3

If the tangent lines to the graph of F at (t, F(t)) and (-t, F(-t)) are perpendicular find t in terms of k.

I don't know where to start really so if someone could walk me through this I'd greatly appreciate it.

Printable View

- January 11th 2010, 12:09 AMNaplesPerpendicular Tangent Lines
F(x) = kx^2 + 3

If the tangent lines to the graph of F at (t, F(t)) and (-t, F(-t)) are perpendicular find t in terms of k.

I don't know where to start really so if someone could walk me through this I'd greatly appreciate it. - January 11th 2010, 12:13 AMbandedkrait
Definition of derivative of F(x) at a given point : It's the slope of the tangent to the graph of F(x) at that point.

So find the derivatives at t and -t, to obtain the slope of the respective tangents at the two points.

Now two lines are perpendicular if their slopes m1, m2 (say.) are such that (m1)(m2) = -1

Use this to find t in terms of k.

Note that you'll have to solve a quadratic equation in t. - January 11th 2010, 12:13 AMProve It