Applications Of Derivatives
The minimum value of f(x)=∣x−1∣+∣x−2∣+...+∣x−2025∣ occurs at:
Select the correct option:
Solution
x=1013
For a function of the form f(x)=∑∣x−ai∣ where ai are sorted increasing order, the minimum occurs at the median of the sequence ai.
Here, the sequence is 1,2,...,2025. The total number of terms is 2025, which is an odd number. The median is the 2n+1-th term. Median position =22025+1=1013.
Thus, the minimum occurs at x=1013.
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About This Question
- Subject
- mathematics
- Chapter
- limit, continuity and differentiability
- Topic
- applications of derivatives
- Difficulty
- Easy
- Year
- 2025
This easy difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of applications of derivatives. It appeared in the 2025 exam. Practice this and similar questions to strengthen your understanding of limit, continuity and differentiability concepts.
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