Provide full work solutions

6. The graph of the derivative function f'(x) of a function f(x) is shown below. Exit Fullscreen 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). + *7. The graphs of the first derivative f'(x) and the second derivative f"(x) of a function f(x) are shown below. Using the graphs, 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 ( 2 , 0) .) y=f *(x) ----- y f "(M) - -.- 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)