If $f(x)=|x+1|+|x+10|$, then find the minimum value of $f(x)$.

The function is of the form $f(x)=|x-a|+|x-b|$. The minimum value of such a function occurs for any $x$ in the interval $[a,b]$ (assuming $a<b$).Here $a=-10$ and $b=-1$.For any $x\in [-10,-1]$:If $x=-5$: $f(-5)=|-5+1|+|-5+10|=|-4|+|5|=4+5=9$.If $x=-1$: $f(-1)=|-1+1|+|-1+10|=0+9=9$.If $x=-10$: $f(-10)=|-10+1|+|-10+10|=|-9|+0=9$.For $x<-10$ or $x>-1$, the value will increase.Therefore, the minimum value is $9$.