Differential Calculus (id: a3e6bc049)

本题目来源于试卷: Differential Calculus，类别为 IB数学

[问答题]
Consider $f(x)=x \ln (x)-x$ , for x>0
1. Find f(1) .
2. Solve f(x)=0 .

The graph of f has a local minimum at point $\mathrm{P}(x, y)$ .
3. Find the coordinates of point P and explain why it is a local minimum.
4. Find the set of x values for which f is increasing.
5. Hence, sketch the graph of f , for x>0 .

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