Q16. [8 points] After long computations, we find the following information about a function f(x). . The domain of f, f', and f" is {re R : x / 1} . f'(x) = 0 for r = -1, r =2, x =4 . f"(x) = 0 for r = -2, x = 3 . lim f(x) = -00 . lim f(x) = -1 and lim f(x) = o r-+- I-+00 Here is a summary of information about the signs of its first and second derivatives: interval x4 sign of f' + + + + sign of f" + + + a) Identify the intervals of increase/ decrease of f. b) Does f have any local minima? If so, give each of the r-values at which f attains a local minimum. c) Does f have any local maxima? If so, give each of the r-values at which f attains a local maximum. d) Identify the intervals of on which f is concave up/down. e) Does f have any inflection points? If so, give each of the r-values at which f has an inflection point. f) Does f have any vertical/horizontal asymptotes? If so, identify each horizontal asymptote and each vertical asymptote. g) From all of the above, sketch the graph of a function whose behaviour matches that of f, as established in parts a)-f). Label each of the special x-values (local extrema or inflection points) and asymptotes you've iden- tified in the preceding parts.