本题目来源于试卷: Integral Calculus，类别为 IB数学
[问答题]
Consider the function defu*d p::.*a wcek 9+gufv;yvv ifl n6wc)a: yz6.ulf n1ined by $f(x)=(1-x) \sqrt{2 x-x^{2}}$ where $0 \leq x \leq 2$ .
1. Show that f(1-x)=-f(1+x) , for $-1 \leq x \leq 1$ .
2. Find $ f^{\prime}(x)$ .
3. Hence find the x -coordinates of any local minimum or maximum points.
4. Find the range of f .
5. Sketch the graph of y=f(x) , indicating clearly the coordinates of the x -intercepts and any local maximum or minimum points.
6. Find the area of the region enclosed by the graph of y=f(x) on the x -axis, for $0 \leq x \leq 1 $.
7. Show that $\int_{0}^{2}|f(x)| d x>\left|\int_{0}^{2} f(x) d x\right|$ .
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