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(2 points) Please answer the following questions about the function /(x) = - 3x2 x2 - 25 Instructions: . If you are asked for a function, enter a function. . If you are asked to find x- or jevalues, 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 an interval or union of intervals, use interval notation. Enter { } if an interval is empty. . If you are asked to find a limit, enter either a number, I for co, -| for -oq or DIVE 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. f'(x) = Critical numbers x = Union of the intervals where /(x )is increasing Union of the intervals where /(x)is decreasing Local maxima x = Local minima x = (b) Find the following left- and right-hand limits at the vertical asymptote x = -5 3.x Jim 3x2 x-+-5 x2 - 25 Find the following left- and right-hand limits at the vertical asymptote x = 5 3x2 1 +5 x2 - 25 lim x-+3+ x2 - 25 Find the following limits at infinity to determine any horizontal asymptotes. 3x2 3x2 lim x-+-ce x2 - 25 lim x-too x2 - 25 (c) Calculate the second derivative of f. Find where f is concave up, concave down, and has inflection points. S'(x) = Union of the intervals where f(x)is concave up Union of the intervals where /(x)is concave down Inflection points x = (d) The function f is ? : because ? for all x in the domain of f, and therefore its graph is symmetric about the (7 (e) Answer the following questions about the function f and its graph. The domain of f is the set (in interval notation) The range of f is the set (in interval notation) J-intercept x-intercepts