Help with old AP Calculus problems?

[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!

 

[mathwonk]

1. try it for x^2.3. remember that |x| is just x when x >0.,,,,

 

[demersal]

thanks for replying, mathwonk.

i gave it a shot with y = x^2 but i still can't get the next step. I'm thinking i need a little more than a shove than a push. haha. if only i was more of left-brain thinker ...