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1. The problem statement, all variables and given/known data

Consider the function F(x) = kx^2 + 3.

a.) 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.

b) Find the slopes of the tangent lines mentioned in part (a).

c.) Find the coordinates of the point of intersection of the tangent lines mentioned in part (a).

2. Relevant equations

1.) First Derivative

2.) Algebraic Manipulation

3. The attempt at a solution

I need to verify my answers. I HAVE SCANNED ALL OF MY ANSWERS SO YOU CAN READ IT EASIER. http://carlodm.com/calc/prob1.jpg [Broken].[/URL]

Here are my questions:

For a.) I got t = +- sqrt( 1 / 4k^2)). I chose the positive root but is this correct? I mean, I chose the positive root to make my calculations simpler but is there a good reason why to choose the positive, or negative?

For b.) Is this algebraic manipulation legitimate?

For c.) This seems a little weird for me considering its not a "finite" answer. Does this answer work? Thank you!!!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Given F(x) = kx^2 + 3 and that F(x) is perpendicular Calculus BC - Algebraic Prob

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