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) = 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. You 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 answer.