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Formulas and tips for Calculus1
One Sided LimitsShow that the side you are evaluating exists | If it is defined @ value plug it in |
First/ Second Derivative TestsFirst | Second | 1. Take derivative and find c.v. | 1. Take and find c.v. | 2. Use a sign chart | 2. Use a sign chart | + is inc. / - is dec. | + is CC up / - is CC down | shows extrema | shows inflection points | * test endpoints | *if checking extrema sign is the opposite |
Derivative of an Integral
| | Limit Definition of Derivatives
| | Intermediate Value TheoremIF f is a function that is continuous over the interval [a,b] and m is some number between f (a) and f (b), THEN there exists a number c between and b such that f (c)=m. |
Rolle's Theorem| | IF: | - [a,b] is continuous | | | - (a,b) is differentiable | | | - f(a)=f(b) | THEN: | f'(c)=0 |
Related Rates1. Draw a picture and label | 2. Use formula for area/volume of shape | 3. Take derivative of formula | 4. Plug in values to each formula as needed | *One variable will NOT have a rate of change (ex. ladder) |
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