This is a big question, but with an easy answer

First, we need to find a spot where the tangent line is parallel to the secant line from #x=-1# and #4#. To have a parallel tangent line, the slope of the tangent line (or derivative) has to be the slope of the secant line. Just by looking at the graph, #y# is a horizontal, because #sqrt(3)# is a constant. The slope of the secant line will be 0, because nowhere on the curve ever changes in #y# value. That means that we need to find a spot where the derivative is #0#, or just about anywhere on the curve, because

#d/dx(c)=0#, assuming #c# is a constant. So, the answer could be anything.