2. (9+6 pts) Given $f(x) = x^{-2} \ln x$, a) Find the critical numbers of $f$ in the open interval $[ rac{1}{2}, 4]$. b) Find the absolute maximum and absolute minimum values of $f$ on the close interval $[ rac{1}{2}, 4]$.
Added by Marcos C.
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Step 1
First, let's find the derivative of f(x). The derivative of x is 1, and the derivative of ln(x) is 1/x. So, the derivative of f(x) is: f'(x) = 1 - 2/x To find the critical numbers, we need to solve the equation f'(x) = 0. 1 - 2/x = 0 To solve this equation, Show more…
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