Let g be a function that is defined for all x, x≠2, such that g(3=4 and the derivative of g is g′(x)=
x2–16
x−2
, with x ≠ 2.
Find all values of x where the graph of g has a critical value.
For each critical value, state whether the graph of g has a local maximum, local minimum or neither. U must justify your answers with a complete sentence.
On what intervals is the graph of g concave down? Justify your answer.
Write an equation for the tangent line to the graph of g at the point where x = 3.
Does this tangent line lie above or below the graph at this point? Justify your answe

Question

Let g be a function that is defined for all x, x≠2, such that g(3=4 and the derivative of g is g′(x)=
x2–16
x−2
, with x ≠ 2.
Find all values of x where the graph of g has a critical value. 
For each critical value, state whether the graph of g has a local maximum, local minimum or neither. U must justify your answers with a complete sentence. 
On what intervals is the graph of g concave down? Justify your answer. 
Write an equation for the tangent line to the graph of g at the point where x = 3. 
Does this tangent line lie above or below the graph at this point? Justify your answe