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# Calculus Rules

### Rules Learned in Calc I

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If f is ____ on the closed interval [a,b], then f attains ___ and ___ in [a,b] continuous, absolute max, absolute min
f(x) has an inflection point at x=c if ___. f changes concavity at c.
f(x) has a critical point at x=c, if ___ or ___. f'(c)=0 or DNE
If f'(x) is greater than 0 on Interval I, then f is ___. increasing on I
If f'(x) is less than 0 on interval I, then f is ___. decreasing on I
If f''(x) is less than 0 on Interval I, then f'(x) is ___ and f is ___. decreasing, concave down
If f''(x) is greater than 0 on Interval I, then f'(x) is ___ and f is ___. increasing, concave up
x=c is an inflection point if ___. the concavity changes
f(c) is an absolute max on I if ___. f(c) is greater than f(x) for all values x in I.
f(c) is an absolute min on I if ___. f(c) is less then f(x) for all values x in I.
f(c) is a local max if ___. f(c) is greater than f(x) for all x near c.
f(c) is a local min if ___. f(c) is less than f(x) for all x near c.
Assume that c is a critical point of f and that f is continuous at x=c. 1. If f'(x) changes from positive to negative, then c is ___. 2. If f'(x) changes from negative to positive, then c is ___. 3. If f'(x) does not change sign, then c is ___. 1. Local max 2. Local min 3. Neither local max nor local min
Assume f'' is continuous near c. 1. If f''(c) is greater than 0, then f(c) is ___. 2. If f''(c) is less than 0, then f(c) is ___. 1. Local max 2. Local min
If f is ___ on a closed interval (a,b), then there exists a c in (a,b), such that ___. continuous, f'(c)=f(b)-f(a)/b-a
If f and g are ___ and ___ near a, and the limit of f(x)/g(x) as x approaches a gives an indeterminate form of ___ or ___, then ___. continuous, g does not equal 0, infinity/infinity. 0/0, limit as x approaches a is f'(x)/g'(x)
A function f is continuous at a number a if ___. The limit of f(x) as x approaches a = f(a)
Suppose that f is ___ on the closed interval [a,b] and let N be any number between f(a) and f(b) where ___. Then there exists a number c in (a,b), such that ___. continuous, f(a) does not equal f(b), f(c)=N
The line x=a is a vertical asymptote when ___. The limit of f(x) as x approaches a is infinity or negative infinity.
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