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

In the interval $(7, \infty) f(x)=|x-5|+2|x-7|$ is
  1. increasing function
  2. decreasing function
  3. constant function
  4. Cannot be estimated

Solution

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

Asked in: AP EAMCET 2022 (05 Jul Shift 2)

Practice more Applications of Derivatives questions on Aicharya