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)={x^2–16}/{x−2}, with x ≠ 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.

Answer 1

Question #1 is x=-44
Question #2 is both points are a local minimum
Question #3 is g''=(x^2-4x+16)/(x-2)^2 since g'' is never negative, g is never concave down
Question #4 is y-4=-9(x-3)
Question #5 is since the graph is always concave up, any tangent lines muse lie below the graph.

I hope that helped