The sum of all local minimum values of the function is [2025]

Question

The sum of all local minimum values of the function $f (x) = {\begin{matrix} 1 - 2 x, & x < - 1 \\ \frac{1}{3} (7 + 2 | x |), & - 1 \leq x \leq 2 \\ \frac{11}{18} (x - 4) (x - 5), & x > 2 \end{matrix}$ is [2025]

Smart Achievers · Accepted Answer

(4)

Graph of the function f(x)

The sum of local minimum values at A and B

$= \frac{7}{3} - \frac{11}{72} = \frac{157}{72}$ .

Solution

Q.
The sum of all local minimum values of the function $f (x) = {\begin{matrix} 1 - 2 x, & x < - 1 \\ \frac{1}{3} (7 + 2 | x |), & - 1 \leq x \leq 2 \\ \frac{11}{18} (x - 4) (x - 5), & x > 2 \end{matrix}$ is [2025]

1 $\frac{131}{72}$

2 $\frac{171}{72}$

3 $\frac{167}{72}$

4 $\frac{157}{72}$

Ans.
(4)

Graph of the function f(x)

The sum of local minimum values at A and B

$= \frac{7}{3} - \frac{11}{72} = \frac{157}{72}$ .

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Solution

Q. The sum of all local minimum values of the function f(x)={1–2x,x<–113(7+2|x|),–1≤x≤21118(x–4)(x–5),x>2 is [2025]

1 13172

2 17172

3 16772

4 15772

Ans. (4) Graph of the function f(x) The sum of local minimum values at A and B =73–1172=15772.