Consider the function f (x) = 2 cos a: + sin2 x, 0 S a; S 271'. (i) (ii) Find (a) local extrema and inection points, (b) all intervals over which f (x) is increas- ing or decreasing, and (c) intervals where f (x) is concave up and down. You should use the First Derivative Test and the Second Derivative Test when determining the be- haviour of the function on the intervals found, and nature of local extrema. Note: the classication of endpoints if they are included in the interval over which the function is dened. Hint: You may use the Trigonometric Identity: cos2 a; sin2 a; = cos(2x). 2 4 The following is also given, f\"(x) = 0 at 00 = {0,312 g}. Using a suitable mathematical graphing tool, sketch the graph of the function then label all the intervals and points found in (i). ' '