Please answer the following clearly and neatly, I would prefer typed out answers and screenshots of graphs. Make sure to show ALL your steps.

1. a) Describe the graph of f(x) using the terminology: MK Exit Fullscreen increasing, decreasing, local maximum or local minimum points, intercepts, and the following information i. f'(x) 2; iv. f(0) = 3, f(1) = 0, f(3) = 0. b) Sketch the graph of f(x). 2. The graph of f(x) has the following properties: i. f(x) is increasing when x 1; ii. f(x) is decreasing on the interval -1 0. a) Describe and sketch a graph of f'(x). b) Explain why there is more than one possible graph for f'(x). 3. a) Use the graph of the derivative g'(x) shown below and the terminology: increasing, decreasing, local maximum or local minimum points, and intervals of concavity, to describe the graph of g(x). b) Explain why there is more than one possible graph for g(x). y=g' (9) X4. Determine the intervals on which the function with equation y = x3 + 6x- + 9x + 2 is increasing. Show your work. 5. Determine the local maximum and local minimum points for the function f(x) = 2x3 + 3x2 - 12x + 3. Show your work. 6. The graph of the derivative function f'(x) of a function f(x) is shown below. a) Determine: i. the intervals where f(x) is increasing; ii. the intervals where f(x) is decreasing; iii. the x -coordinate for all local extrema of f(x); iv. the x -coordinate for the point of inflection; v. the intervals of concavity. b) If f(0) = 1, sketch a graph of f(x)