Finding Inflection Points Answer the questions in the scenarios below, then compare your answer with those of your group members and discuss any differences. Scenario 1: Suppose that f (x) = x* + x3 -3x2. a. Find the first and second derivatives of f (x). b. Does f (x) have any inflection points? If it does, find their coordinates and explain why they are inflection points. Scenario 2: Suppose that g (x) = +. Then the first derivative, g'(x), is x" + 2x' + 3x2 -4x -2 x? + x+1 (x2 + x+ 1)? and the second derivative, g"(x) , is 18x(x+1) (x7 + x+1)' . Does g(x) have any inflection points? If it does, find their coordinates and explain why they are inflection points. Scenario 3: This is a graph of the derivative of h(x), which is a function defined and continuously differentiable on the interval [A,G] . Use this graph of y = h'(x) to answer the following questions. X X=AX=B X=C X=DI X=FI X=E X=G The graph of y = h'(x) a. What are the x-coordinates of the inflection points of h(x) ? b. Justify why those x-values are inflection points