g has a critical value where g'=0: x = ±4
max/concave down if g" < 0
g" = (x^2-4x+16)/(x-2)^2
For the tangent line, you have a point (3,4) and a slope (-7), so the line is
y-4 = -7(x-3)
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? Justify your answer.
1 answer
1 answer