Q1 (12 points) Consider the curve given by the function f(a) with a 2 and -2....

 

 

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Q1 (12 points) Consider the curve given by the function f(a) with a 2 and -2. You are given that f'(x) = -3x-4 (x - 4) and f" (x)= 12x(x+4) (x-4)4 D-Logo Compile the following information about f(x). Show your work to justify your answers to parts (a), (b), (c), (d) and (e). [2] Find the critical number(s) of f and show your work to justify. [3] Find the open interval(s) where f is increasing and the open interval(s) where f is decreasing. Show your work to justify. [2] Find the x- coordinate(s) of all local maxima of f, and all local minima of f. Show your work to justify. [3] Find the open intervals where f is concave up and the open intervals where f is concave down. Show your work to justify. [2] Find the x-coordinate(s) of all inflection point(s), and show your work to justify. Q1 (12 points) Consider the curve given by the function f(a) with a 2 and -2. You are given that f'(x) = -3x-4 (x - 4) and f" (x)= 12x(x+4) (x-4)4 D-Logo Compile the following information about f(x). Show your work to justify your answers to parts (a), (b), (c), (d) and (e). [2] Find the critical number(s) of f and show your work to justify. [3] Find the open interval(s) where f is increasing and the open interval(s) where f is decreasing. Show your work to justify. [2] Find the x- coordinate(s) of all local maxima of f, and all local minima of f. Show your work to justify. [3] Find the open intervals where f is concave up and the open intervals where f is concave down. Show your work to justify. [2] Find the x-coordinate(s) of all inflection point(s), and show your work to justify.