Calculus BIBLE

Calculus BIBLE - min max his is the graph of f(x). Make a...

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min max x = -4, 3 x = 0 increasing decreasing (-4,0) (3,6] [-6,-4] (0,3) This is the graph of f’ ( x ). Make a number line. Where f’ ( x ) = 0 (x-int) is where there are possible max and mins. Signs are based on if the graph is above or below the x-axis (determines increasing and decreasing) Signs are determined by if f’ ( x ) is increasing (+) and decreasing (-) The Calculus AB Bible The 2nd most important book in the world Derivative Formulas Derivative Notation: For a function f(x) , the derivative would be Leibniz's Notation: For the derivative of y in terms of x , we write For the second derivative using Leibniz's Notation: Product Rule: Quotient Rule: Chain Rule:
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Natural Log Power Rule: Constant with a Variable Power: Variable with a Variable power Take ln of both sides!
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Implicit Differentiation: Is done when the equation has mixed variables : Trigonometric Functions: Inverse Trigonometric Functions:
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Integral Formulas Basic Integral , where C is an arbitrary constant Variable with a Constant Power Constant with a Variable Power Fractions if the top is the derivative of the bottom -unless-
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When integrating a product in which the terms are somehow related, we usually let u = the part in the parenthesis, the part under the radical, the denominator, the exponent, or the angle of the trigonometric function Integration by Parts When taking an integral of a product, substitute for u the term whose derivative would eventually reach 0 and the other term for dv . The general form:
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This note was uploaded on 04/01/2010 for the course MATH 135 taught by Professor Noone during the Spring '08 term at Rutgers.

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Calculus BIBLE - min max his is the graph of f(x). Make a...

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