Please provide clear explanation for the problems. Thank you so much.

If f: R -> R is a differentiable function, whose graph never crosses the x-axis, then we can definitely conclude that... (Choose all that apply.) .. f has no horizontal tangent lines. J .. f has no vertical tangent lines. ..f' never crosses the x-axis. O .. f' must cross the x-axis at least once. .. f has no points of discontinuityAssume the functions f and g are differentiable functions, with f(1) =6, f' (1) =-2. g(1)=-1 and g'(1) = 3. f(x) + 3x Find an equation of the line perpendicular to the graph of F(z) = at 2 - g(x) c=1