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Please answer the following questions about the function f(x ) = = 672 72 - 4 Instructions: If you are asked for a function, enter a function. If you are asked to find a- or y-values, enter either a number or a list of numbers separated by commas. If there are no solutions, enter None. If you are asked to find intervals of increase/decrease/concavity, please separate the lists with commas and NOT the union symbol. For the domain and range, use interval notation and NOT commas. If you are asked to find a limit, enter DIE if the limit does not exist. (a) Calculate the first derivative of f. Find the critical numbers of f, where it is increasing and decreasing, and its local extrema. 48x f'(x) = ( x 2 - 4 ) 2 Critical numbers z = 0 List of the intervals where f() is increasing (separated by commas and NOT the union symbol) List of the intervals where f() is decreasing (separated by commas and NOT the union symbol) Local maxima I Local minimaz =[ (b) Find the following left- and right-hand limits at the vertical asymptote z = -2 2 7-2 12 -4 ? lim 1 -2+ 12 - 4 = ? Find the following left- and right-hand limits at the vertical asymptote z = 2. y-intercept 672 672 2 72 - 4 lim v Find the following limits at infinity to determine any horizontal asymptotes. -intercepts lim +00 22 -4 ? 1+00 72 - 4 (c) Calculate the second derivative of f. Find where f is concave up, concave down, and has inflection points. f" (I) =0 List of the intervals where f() is concave up (separated by commas and NOT the union symbol) (f) Sketch a grap List of the intervals where f() is concave down (separated by commas and NOT the union symbol) Inflection points = = horizontal and v (d) The function f is ? because ? for all a in the domain of f, and therefore its graph is symmetric about (e) Answer the following questions about the function f and its graph. parts of the gra The domain of f is the set (in interval notation and NOT using commas ) The range of f is the set (in interval notation and NOT using commas ) y-intercept exams