64. An object with weight W is dragged along a horizontal plane by a force acting on a rope attached to the object. If the rope makes an angle 0 with the plane, then the magnitude of the force is F = H sin(0) + cos(0) where u is a positive constant called the coefficient of friction and where 0 $ 0 S w/2. Show that F is minimized when tan(0) = #. 68. Explain why 5 is a critical number of the function 9(x) = 2+ (x -5)" but g does not have a local maximum or local minimum at 5. 70. If f has a local minimum value at c, use computations and words to explain why the function g(x) = -f(x) has a local maximum value at c