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Unformatted text preview: have a local max. If the second derivative is positive, you have a local min. Graphing a Function: Find all the following information about your function and then graph it. 1. Domain: legal x‐values 2. Symmetry: Odd: 3.
5. 6. 7. f ( x) f ( x) , symmetric about the origin, Even: f ( x) f ( x) , symmetric about the y‐axis, Periodic: f ( x k ) f ( x) for all x, period is k Derivatives: Find the first and second derivative f ( x) and f ( x) equal 0 or are undefined. Increasing\Decreasing: Draw a f ' number line. f '( x ) 0 f is increasing, f '( x ) 0 f is decreasing Concavity: Draw a f number line. f ( x ) 0 f is concave down, f ( x ) 0 f is concave up Max/Min: Relative Extrema occur if f '( x ) changes sign and f (x) is continuous at the point Inflection Points: Inflection points occur if f ( x ) changes sign and f(x) is defined at the point Critical Points and Inflection Points: Where Asymptotes: Vertical Asymptot...
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This note was uploaded on 02/24/2014 for the course MATH 1151 taught by Professor Daniel during the Fall '12 term at Ohio State.
- Fall '12