Q108 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Mathematics

In the interval $(7, \infty) f(x)=|x-5|+2|x-7|$ is

  • Correct answer
    A
    increasing function
  • B
    decreasing function
  • C
    constant function
  • D
    Cannot be estimated

Solution

$|x-5|=$ $\begin{cases}x-5, & x \geq 5 \\ -(x-5), & x < 5\end{cases}$ $x>7$ $f(x)=x-5+2(x-7)$ $=3 x-5-14$ $\begin{aligned} & f(x)=3 x-19 . \\ & f^{\prime}(x)=3>0\end{aligned}$

Hence, the correct answer is option: 'A'.

Relevant Questions