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Miss Battaglia AP Calculus AB/BC A function f is increasing on an interval for any two numbers x1 and x2 in the interval, x1<x2 implies f(x1)<f(x2) A function f is decreasing on an interval for any two numbers x1 and x2 in the interval, x1<x2 implies f(x1)>f(x2) Increasing! Pierre the Mountain Climbing Ant is climbing the hill from left to right. Decreasing! Pierre is walking downhill. Let f be a function that is continuous on the closed interval [a,b] and differentiable on the open interval (a,b). 1. 2. 3. If f’(x)>0 for all x in (a,b), then f is increasing on [a,b] If f’(x)<0 for all x in (a,b), then f is decreasing on [a,b] If f’(x)=0 for all x in (a,b), then f is contant on [a,b] Find the open intervals on which f (x) = x 3 - 3 x 2 is 2 increasing or decreasing. Find the first derivative. Set the derivative equal to zero and solve for x. Put the critical numbers you found on a number line (dividing it into regions). Pick a value from each region, plug it into the first derivative and note whether your result is positive or negative. Indicate where the function is increasing or decreasing. 1 Find the relative extrema of the function f (x) = x - sin x 2 in the interval (0,2π) Find the relative extrema of f (x) = (x 2 - 4)2/3 x 4 +1 Find the relative extrema of f (x) = 2 x Read 3.3 Page 179 #1, 8, 12, 21, 27, 29, 35, 43, 45, 63, 67, 79, 99-103