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!