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Help with old AP Calculus problems?

  1. Oct 15, 2007 #1
    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!

    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).

    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.

    Last edited: Oct 16, 2007
  2. jcsd
  3. Oct 15, 2007 #2


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    1. try it for x^2.

    3. remember that |x| is just x when x >0.,,,,
  4. Oct 15, 2007 #3
    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 ...
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