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# Extrema

How can you maximize your happiness under a budget? When does a function reach its minimum value? When does a curve change direction? The calculus of extrema explains these "extreme" situations.

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What is the positive number \(x\) that maximizes \( 9 \cdot {x}^{\frac{1}{x}}+10? \)

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For what value of \(x\) is the function \(f(x) = 7 x^2 - 84 x + 19\) minimized?

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What is the absolute value of the minimum value of the function \(f(x)=x^4-24 x^2 + 64 x + 16\)?

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What is the extreme value of \( f(x) = |x-1| + 22\)?

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For what value of \(x\) is the function \(f(x) = x^4 - 36 x^3 + 20\) minimized?

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