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Maximizing a function - mechanical

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What value of x will maximize: r(x)=r^2*(ln(1/x)? x can take values between
1/4 and 1

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We first take the derivative of r(x) wrt x and then set it equal to zero. Then solve this equation for x and this gives the value of x that will ...

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The solution contains a step by step solution to maximizing a function. The solution is detailed in words as well as equations.