__ _ " ..ucuuuuununuuulm u umgla ' W Log (20 points) Sketch the graph of a single function f(a:) over the interval that satisfies all of the following conditions. Find critical numbers for f' (to) and f\" (m) and show sign charts for both functions. Indicate the intervals where f (:13) is increasing. decreasing. concave up and concave down. Label all local maxima, local minima. and inflection points. Show asymptotes using dashed lines. (i) at) is defined and continuous for all values of a: on the interval [0, 271']. (ii) f' (at) = 1 + 2 cos :1: (iii) f\"(:r:) = 2 sine: (iv) f(0) = 0 (v) for) 96 31 (vi) f(27r) :3 6.3