Answer all the following questions. this is about inflection points and answer it with number line and graphs as needed. Write it up in a piece of paper and step by step on how to answer all the questions.

AP CALCULUS Justifying Inflection Points Some values of a twice differentiable function, f(x) , and its first and second derivatives, f'(x) and f"(x) respectively, are given in the table below. For example, f'(3) - -2. Use the table to answer the questions that follow. 2 3 4 THX A(x ) 5 2 0 -2 0 MX f" (x ) 2 0 -3 1. Does A(x) = (f (x))? have a critical point at x = 4? If A(x) does have a critical point, can you determine whether it is a local maximum, local minimum, or neither? Explain your answer. 2. Does B(x) = f(x2) have a critical point at x = 2? If B(x) does have a critical point, can you determine whether it is a local maximum, local minimum, or neither? Explain your answer. Does C(x) = f(f (x)) have a critical point at x = 3? If C(x) does have a critical point, can you determine whether it is a local maximum, local minimum, or neither? Explain your answer. 4. Does D(x) = f(4x -2) have a critical point at x = 1? If D(x) does have a critical point, can you determine whether it is a local maximum, local minimum, or neither? Explain your answer. 5. Does E (x) = f(x+3) have a critical point at x = 0? If E(x) does have a critical point, can you determine whether it is a local maximum, local minimum, or neither? Explain your answer. CollegeBoard 2017 College Board