The sum of all local minimum values of the function
$f(x)=\left\{\begin{array}{lr}
1-2 x, & x \lt -1 \\ \frac{1}{3}(7+2|x|), & -1 \leq x \leq 2 \\ \frac{11}{18}(x-4)(x-5), & x \gt 2
\end{array}\right.$
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Question

Aicharya · Accepted Answer

$f(x)=\left\{\begin{array}{cl}1-2 x, & x < -1 \\ \frac{1}{3}(7-2 x), & -1 \leq x \leq 2 \\ \frac{1}{3}(7+2 x) & 0 \leq x < 2 \\ \frac{11}{18}(x-4)(x-5), & x>2\end{array}\right.$

$\therefore$ Local minimum values at $\mathrm{A} \& \mathrm{~B}$
$\begin{aligned}
& \frac{7}{3}-\frac{11}{72} \\ & \Rightarrow \frac{168-11}{72} \Rightarrow \frac{157}{72}
\end{aligned}$

The sum of all local minimum values of the function $f(x)=\left\{\begin{array}{lr} 1-2 x, & x \lt -1 \\…

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