Question

Let g be a function that is defined for all x, x cannot = 2, such that g(3) = 4 and the derivative of g is g1(x)=


x2-16/x-2

, with x not = 2.

1.Find all values of x where the graph of g has a critical value.



2.For each critical value, state whether the graph of g has a local maximum, local minimum or neither. You must justify your answers with a complete sentence.



3.On what intervals is the graph of g concave down? Justify your answer.



4.Write an equation for the tangent line to the graph of g at the point where x = 3.


5.Does this tangent line lie above or below the graph at this point? Justify your answer