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f(x)f(x)f(x) is increasing if f(x1)≤f(x2)f(x_1) \leq f(x_2)f(x1)≤f(x2) for x1<x2x_1 < x_2x1<x2.
f(x)f(x)f(x) is decreasing if f(x1)>f(x2)f(x_1) > f(x_2)f(x1)>f(x2) for x1<x2x_1 < x_2x1<x2.
f(x)f(x)f(x) is strictly increasing if f(x1)<f(x2)f(x_1) < f(x_2)f(x1)<f(x2) for x1<x2x_1 < x_2x1<x2.
f(x)f(x)f(x) is strictly decreasing if f(x1)>f(x2)f(x_1) > f(x_2)f(x1)>f(x2) for x1<x2x_1 < x_2x1<x2.
f′(x)>0f'(x) > 0f′(x)>0 means f(x)f(x)f(x) is increasing; f′(x)<0f'(x) < 0f′(x)<0 means decreasing.
Critical points occur where f′(x)=0f'(x) = 0f′(x)=0 or is undefined.
Use test points in intervals defined by critical points.
f(x)f(x)f(x) is constant on intervals where f′(x)=0f'(x) = 0f′(x)=0.
Calculate the first derivative f′(x)f'(x)f′(x) of the function.
Finding local maxima or minima using increasing/decreasing info.
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