Exercise 1.
\(f(x)=x^2-10x+9\text{,}\) on the interval \(0\le x\le 10\text{.}\)
Solution.
- We can read off the roots from the table \(f(x)=0\) at \(x = 1\) and at \(x = 9\)
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Use Solver to find the minimum.Solver indicates that the minimum value of the function is -16 and the minimum takes place at \(x = 5\text{.}\)We have local maximums at the endpoints \((0, 9)\) and \((10,9)\text{.}\)
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Test the endpoints,\((0, 9)\) and \((10,9)\text{,}\) and compare to the minimum, \((5, 16)\text{.}\)The absolute minimum is -16 (at \(x = 5\)) and the absolute maximum is 9 (at \(x = 1\) and 10)