Consider the equation below. F(x) = 6 sin(x) + 6 cos(x), 0 s x s 2n (a) Find the interval on which fis increasing. Find the interval on which fis decreasing. (b) Find the local minimum and maximum values of f. (c) Find the inflection points. Find the interval on which fis concave up. Find the interval on which fis concave down. Step 1 (a) Find the interval on which fis increasing. Find the interval on which fis decreasing. For f(x) = 6 sin(x) + 6 cos(x), we have F'(x) = -6( sin(x) - cos(x) 6 cos(ar) - 6sin(x) If this equals 0, then we have cos(*) = sin(x) . which becomes tan(x) = 1 4 57 sin(x) 1 . Hence, in the interval 0 s x s 21, f'(x) = 0 when x = _ or x = 4 Step 2 If f'(x) is negative, then f(x) is decreasing decreasing . If f'(x) is positive, then f(*) is increasing increasing Step 3 If 0