Consider the equation below. f(x) = 6 sin(x) + 6 cos(x), 0 sxs 2n Exercise (a) Find the interval on which f is increasing. Find the interval on which f is decreasing. Step 1 For f(x) = 6 sin(x) + 6 cos(x), we have f'(x) = 6 cos (x) – 6 sin (x 6 cos (x) – 6 sin(x) If this equals 0, then we have cos(x) = sin (x) sin(x) which becomes tan(x) = Hence, in the interval 0 s x s 27, f'(x) = 0 when x = or 57 X = 4 4 Step 2 If f'(x) is negative, then f(x) is decreasing decreasing. If f'(x) is positive, then f(x) is increasing increasing Step 3 If 0

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