Question

5. Find the open intervals on which f(x) =x^3−6x^2−36x+ 2 is increasing, as well as the open intervals on which f(x) is decreasing.

- How do you know when the function is increasing or decreasing? Please show all work.

6. Find the open interval on which f(x) =x^3−6x^2−36x+ 2 has upward concavity, as well as the open intervals on which f(x) has downward con-cavity.

- How do you know if a function has an upward concavity or downward concavity? Please show all work.

7. Find all x-values at which local extrema of f(x) =x^3−6x^2−36x+ 2 occur. Indicate whether each extremum is a maximum or a minimum.

- How do you know if the value you have is a minimum or maxiumu? Please show all work.

8. Sketch the graph of f(x) =x3−6x2−36x+ 2. Your graph does not need to be precise, but it should have the correct basic shape based on your answer to Problems 5-7

Please show all work.

Answer 1