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

7. The graphs of the first derivative f'(x) and the second derivative f"(x) of a function f(x) are shown below. >sing thesgraphs, determine the x -coordinate for all the local extrema of f(x). (Note that point labelled on the graph may be difficult to read and is intended to be ( 3 , 0) .) y TPq .-.- 8. Use calculus and algebraic methods to do a complete analysis (i.e., intervals of increase and decrease, intercepts, critical points, points of inflection, and intervals of concavity) for each of the following functions and then use technology to draw the graph of the function and verify your analysis. a ) f(x) = x3 - 3x2 b) g( x) = (x - 2)3 ( x - 6 ) 9. The function h(x) = x3 + bx2 + d has a critical point at (2, -4). Determine the constants b and d and find the equation of h(x). Show your work. 10. The graph of f(x) is shown below. a) Determine: i. the intervals of increase and decrease; ii. the x -coordinate for all local extrema; iii. the intercepts. b) Draw the graph of f'(x).11. A ball is projected upward from the ground. The velocity vs time graph is shown below. a) What is the initial velocity of the ball? b) How long does it for the ball to reach its maximum height? 25 | v (m/s) (0,19.6) t (5) H#########+