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maximum or minimum

maximum or minimum - ± Positive result means concave up =...

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To maximize or minimize something: 1. You need a function. ° The function might be given. ° You might need to create the function. 2. Find the stationary points for the function by finding its derivative, and setting the derivative = 0. ° Maximum and minimum values for the function must occur at its stationary points OR could be at the endpoints if you working within a specified interval. 3. Determine if the stationery points yield maximum or minimum values for the function. ° You can do this by checking out the graph if possible. ° You can also use the Second Derivative Test. o Find the 2 nd derivative. o Plug in the stationery points into the 2 nd derivative and see if the result is positive or negative.
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Unformatted text preview: ± Positive result means concave up = min ± Negative result means concave down = max & You can also determine whether the function is increasing (derivative is positive) or decreasing (derivative is negative) to the right and left of any stationary point. o If the derivative is positive, then changes to negative on either side of a stationery point, you have a local maximum. o If the derivative is negative, then changes to positive on either side of a stationery point, then you have a local minimum. o If the derivative doesn’t change sign, it’s neither. 4. If you are dealing with an application problem, be sure to answer the specific question....
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