Steps of sketching curve

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Steps of sketching curve : 

Steps of sketching curve All the steps that you need To take to sketch a curve. 3/22/2010 1

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To find critical points:

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Each critical point has four possibilities: Local Maximum Local Minimum Saddle Point Outside the domain of the original function.

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To determine which critical point is local max, which one is local min and which one is saddle. Also to determine interval of increasing and decreasing:

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A word of caution Sometimes it is possible for a point to be outside the domain of the original function. But still you need to put that point in the number line although it is not going to be a local max, local min, or saddle point. An example will clarify this point later.

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To determine inflection point and interval of Concave up and concave down:

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A word of caution Sometimes it is possible for a possible inflection point to be outside the domain of the original function. But still you need to put that point in the number line although it is not going to be an inflection point. An example will clarify this point later.

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