question_answer

Direction: Sometimes use of graph is very important to find the number of solutions of an equation. To find the number of solutions of the equation \[{{f}_{1}}(x)={{f}_{2}}(x)\]. We drain the graph of\[y={{f}_{1}}(x),\]\[y={{f}_{2}}(x)\] and the number of point of intersection of these graphs is equal to the number of solution. Let us consider the function \[f(x)=\,|x-1|+\,|x-3|+\,|x-7|+|x-13|\]

The minimum value of f{x) is

A)  10                              

B)  16              

C)  20                              

D)  28

Correct Answer: B

Solution :

 \[f(x=\,|x-1|\,+|\,x-3|\,+|\,x-7|\,+|\,x-13|\] at \[x=1,\]        \[f(x)=20\] at \[x=3,\]        \[f(x)=16\] at \[x=7,\]        \[f(x)=16\] at \[x=13,\]      \[f(x)=28\] The min value of \[f(x)\] is 16.