Miss Battaglia AP Calculus AB/BC. A function f is increasing on an interval for any two numbers x 1 and x 2 in the interval, x 1 <x 2 implies f(x 1 )<f(x.

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Presentation transcript:

Miss Battaglia AP Calculus AB/BC

A function f is increasing on an interval for any two numbers x 1 and x 2 in the interval, x 1 <x 2 implies f(x 1 )<f(x 2 ) A function f is decreasing on an interval for any two numbers x 1 and x 2 in the interval, x 1 f(x 2 ) 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. If f’(x)>0 for all x in (a,b), then f is increasing on [a,b] 2. If f’(x)<0 for all x in (a,b), then f is decreasing on [a,b] 3. If f’(x)=0 for all x in (a,b), then f is contant on [a,b]

Find the open intervals on which is 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.

Find the relative extrema of the function in the interval (0,2π)

Find the relative extrema of

 Read 3.3 Page 179 #1, 8, 12, 21, 27, 29, 35, 43, 45, 63, 67, 79,