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\gt2 \end{array}\right.$ $
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f ( x ) = ⎩ ⎨ ⎧ ​ 1 − 2 x , 3 1 ​ ( 7 − 2 x ) , 3 1 ​ ( 7 + 2 x ) 18 11 ​ ( x − 4 ) ( x − 5 ) , ​ x < − 1 − 1 ≤ x ≤ 2 0 ≤ x < 2 x > 2 ​ ∴ Local minimum values at A & B ​ 3 7 ​ − 72 11 ​ ⇒ 72 168 − 11 ​ ⇒ 72 157 ​ ​

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