# Help with old AP Calculus problems?

1. Oct 15, 2007

### demersal

I have been working for over 6 hours trying to break these problems down (my first calc problems!), but I cannot get any major breakthroughs. I have made minor strides in each but have hit a wall. If any of you can offer explanations, work, anything, I would be eternally grateful!

#1
Let h(x) = kx^2 + c
a) Find x sub 0 in terms of k such that the tangent lines to the graph of h at (x sub 0, h(x sub 0)) and (-x sub 0, h(-x sub 0)) are perpendicular.

... I have x = 1/2k. Does that make sense? Ugh, I am so lost.

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

c) Find the coordinates, in terms of k and c, of the point of intersection of the tangent lines mentioned in a.

#2 (couldn't even make a dent)
The line x =c where c > 0 intersects the cubic y = 2x^3 + 3x^2 - 9 at point J and the parabola y = 4x^2 + 4x + 5 at point G.

a) If a line tangent to the cubic at point J is parallel to the line tangent to the parabola at point Q, find the value of c where c > 0.

b) Write the equations of the two tangent lines described in (a).

#3
Let f be the function given by b(x) = (|x| - 2) / (x-2)

b) Find b '(1)

c) Find b '(-1)

d) find the range of b

... For this one I don't know how to find the derivative of an absolute value equation.

THANK YOU!

Last edited: Oct 16, 2007
2. Oct 15, 2007

### mathwonk

1. try it for x^2.

3. remember that |x| is just x when x >0.,,,,

3. Oct 15, 2007