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Related Flashcards
Related Topics
Cards In This Set
| Front | Back |
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Definition of Derivative
(answer as function) |
 See image  |
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Def. of Derivative 2
(answer in values) |
 See image |
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Linear Approximation
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L(x) = f(a) + f'(a)(x-a)
Note: Idea = use tangent line to approximate f at a value close to a. Careful though, this method of approximation does not take into account whether the actual curve lies below or above the tangent line. Error exists!!! |
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Related Rates Recipe
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1) Find all rates, both given and sought
2) Find Static formula to relate the variables 3) Take derivatives of both sides with respect to time |
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Extreme Value Theorem
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If f is continuous on a closed interval [a,b], then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in [a,b]
*Note: To find the absolute extrema: 1) find values of f at all critical numbers (f'(c) = 0) on (a,b) 2) find the values of f at the endpoints |
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Rolle's Theorem
(hint: a special case of MVT) |
If f is continuous on a closed interval [a,b] and differentiable on 9a,b0, and f(a) = f(b), then there exists a number c on (a,b) such that f'(c) = 0.
* basically saying that you'll find a critical number in between x = a and x = b... |
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The Mean Value Theorem
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If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f'(c) = f(b) - f(a) / b-a
*basically saying that the tangent line at x=c has the same slope as the secant line connecting a and b |
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Differential Equations
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Exponential: P =P0 ekt
logistic: dP/dt = kP(1-P/K), K = carrying capacity |
