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 \[f(x)=\,|x-1|+\,|x-3|+\,|x-7|+|x-13|\] |
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.You need to login to perform this action.
You will be redirected in
3 sec