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.

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? Jus

Answer 1

@mathstudent55

Answer 2

@zepdrix @aaronq

Answer 3

@AloneS @jagr2713 @mathmate

Answer 4

@SolomonZelman do you understand this? I'm confused

Answer 5

@mathstudent55

Answer 6

@Kainui