Question:

# A twice differentiable function f is defined for all real

Last updated: 5/22/2023

A twice differentiable function f is defined for all real numbers x The derivative of the function f and its second derivative have the properties and various values of x as indicated in the table 6 f x positive DNE negative 0 f x positive DNE positive 0 X 0 x 3 3 3 x 6 6 x 9 negative negative Part A Find all values of x at which f has a relative extrema on the interval 0 9 Determine whether f has a relative maximum or a relative minimum at each of these values Justify your answer 10 points Part B Determine where the graph of f is concave up and where it is concave down Support your answer 10 points Part C Find any points of inflection of f Show the analysis that leads to your answer 10 points