Day-6-filled - Math 1314 Day 6 Optimization Were interested...

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Math 1314 Day 6 Optimization We’re interested in finding the highest high point or the lowest low point of our function. We call these the absolute extrema. First – over the entire domain of the function. Example 1:
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The graph of a quadratic function will have either an absolute max or an absolute min, but not both. If the leading coefficient is positive, the parabola opens up and the function has a minimum. If the leading coefficient is negative, the parabola opens down and the function has a maximum. Example 1 : Find any absolute extrema: 2 ( ) 3 5 8 f x x x = - +
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Remember some functions have absolute maxima, some have absolute minima and some have neither! Most of the time, you’ll need to find absolute extrema over a closed interval . You can only do this if the function is continuous on that interval. So if there are any asymptotes (zeros in the denominator) you might have a problem. Here’s the process: Finding the Absolute Extrema of f on a Closed Interval 1. Find the critical points of f that lie in (a, b). 2. Compute the value of the function at every critical point found in step 1 and also compute f ( a ) and f ( b ). 3. The absolute maximum value will be the largest value found in step 2, and the absolute minimum value will be the smallest value found in step 2.
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