AP EAMCET · Maths · Application of Derivatives
In the interval \((7, \infty) f(x)=|x-5|+2|x-7|\) is
- A increasing function
- B decreasing function
- C constant function
- D Cannot be estimated
Answer & Solution
Correct Answer
(A) increasing function
Step-by-step Solution
Detailed explanation
\(|x-5|=\) \(\begin{cases}x-5, & x \geq 5 \\ -(x-5), & x 7\) \(f(x)=x-5+2(x-7)\) \(=3 x-5-14\) \(\begin{aligned} & f(x)=3 x-19 . \\ & f^{\prime}(x)=3>0\end{aligned}\)
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