Consider the three analytic functions defined for all real
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Consider the three analytic functions defined for all real x.
g(x)=6x−12h(x)=x3−6x2+9x+4k(x)=3x2−12x+9
Exactly one of these functions is the graph of a differentiable function f, one is the graph of f′, and one is the graph of f′′.
(1) Part 1: Determine which given function is f, which is f′, and which is f′′. Show analytical work that supports your conclusion.
(2) Part 2: For the function you identified as f, determine the interval(s) on which f is increasing and the interval(s) on which f is concave upward.
(3) Part 3: For the function you identified as f, find the coordinates of every point of inflection and justify that each is indeed an inflection point.