JEE Mains · Maths · STD 12 - 6. Application of derivatives
The sum of all local minimum values of the function is
\(
f(x)=\left\{\begin{array}{lr}
1-2 x, & x \lt -1 \\
\frac{1}{3}(7+2|x|), & -1 \leq x \leq 2 \\
\frac{11}{18}(x-4)(x-5), & x\gt2
\end{array}\right.
\)
- A \(\frac{157}{72}\)
- B \(\frac{131}{72}\)
- C \(\frac{171}{72}\)
- D \(\frac{167}{72}\)
Answer & Solution
Correct Answer
(A) \(\frac{157}{72}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cl}1-2 x, & x < -1 \\ \frac{1}{3}(7-2 x), & -1 \leq x \leq 2 \\ \frac{1}{3}(7+2 x) & 0 \leq x < 2 \\ \frac{11}{18}(x-4)(x-5), & x>2\end{array}\right.\) \(\therefore\) Local minimum values at \(\mathrm{A} \& \mathrm{~B}\)…
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