陶哲轩实分析（上）9.6及习题-Analysis I 9.6

这一节是最值定理，即闭区间上连续函数一定可取到最大值和最小值。

Exercise 9.6.1

( a ) $f(x)=|x-3/2|$ attains minimum $0$ at $3/2$, but can’t attain its maximum.
( b ) $f(x)=a^x,0<a<1$ attains it’s maximum $1$ at $0$, but can’t attain its minimum.
( c ) $f(x)=\begin{cases}0, & x=-1\\x, & x∈(-1,1)\\0, & x=1\end{cases}$
( d ) $f(x)=\begin{cases}0, & x=0\\1/x, & x∈[-1,0)∪(0,1]\end{cases}$

For the examples in ( a ) and ( b ), the intervals are not closed.
For the examples in ( c ) and ( d ), the functions are not continuous.