The sum of the absolute maximum and minimum values of the function f ( x ) = | x 2 - 5 x + 6 | - 3 x + 2 in the interval [ - 1 , 3 ] is equal to [2023]

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Solution

Q.
The sum of the absolute maximum and minimum values of the function $f (x) =$ $| x^{2} - 5 x + 6 |$ $- 3 x + 2$ in the interval $[- 1, 3]$ is equal to [2023]

1 12

2 10

3 24

4 13

Ans.
(2)

$f (x) =$ $| x^{2} - 5 x + 6 |$ $- 3 x + 2$

$f (x)$ $=$ ${\begin{matrix} x^{2} - 8 x + 8, & x \in [- 1, 2] \\ - x^{2} + 2 x - 4, & x \in [2, 3] \end{matrix}$

From the graph, Maximum value = 17

Minimum value = - 7 as $f$ (-1) = 17 and $f (3) = - 7$

$∴$ Sum of the absolute maximum and minimum values = $17 - 7 = 10$

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