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Jee Main 2025 — Medium JEE math MCQ

The sum of all local minimum values of the function \[ f(x) = \begin{cases} 1 - 2x, & x < -1 \\ \frac{1}{3}(7 + 2|x|), & -1 \leq x \leq 2 \\ \frac{1}{12}(x - 4)(x - 5), & x > 2 \end{cases} \] is
  1. A. \( \frac{137}{72} \)
  2. B. \( \frac{131}{72} \)
  3. C. \( \frac{137}{72} \)
  4. D. \( \frac{167}{72} \)

Solution

The correct option is **A**. (A. \( \frac{137}{72} \))

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
The sum of all local minimum values of the function f(x)={1−2x,x<−113(7+2∣x∣),−1≤x≤2112(x−4)(x−5),x>2 f(x) = \begin{cases} 1 - 2x, & x < -1 \\ \frac{1}{3}(7 + 2|x|), & -1 \leq x \leq 2 \\ \frac{1}{12}(x - 4)(x - 5), & x > 2 \end{cases} is
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