If m and n be the absolute maximum and minimum values of the function then m+n is

Question

If $m$ and $n$ be the absolute maximum and minimum values of the function $f (x) =$ $| x^{2} - 7 x + 10 |$ $- 5 x + 27, x \in [- 2, 14]$ then $m + n$ is

Smart Achievers · Accepted Answer

(2)

$y =$ $f (x) =$

$y = a x^{2} + b x + c$

Solution

Q.
If $m$ and $n$ be the absolute maximum and minimum values of the function $f (x) =$ $| x^{2} - 7 x + 10 |$ $- 5 x + 27, x \in [- 2, 14]$ then $m + n$ is

1 65

2 66

3 68

4 70

Ans.
(2)

$y =$ ${\begin{matrix} x^{2} - 12 x + 37, & x \leq 2 \\ 2 x - x^{2} + 17, & 2 < x < 5 \\ x^{2} - 12 x + 37, & x \geq 5 \end{matrix}}$

$y = a x^{2} + b x + c$

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Solution

Q. If m and n be the absolute maximum and minimum values of the function f(x)=|x2-7x+10|-5x+27, x∈[-2,14] then m+n is

1 65

2 66

3 68

4 70

Ans. (2) y={x2-12x+37,x≤22x-x2+17,2<x<5x2-12x+37,x≥5} y=ax2+bx+c

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Q.
If $m$ and $n$ be the absolute maximum and minimum values of the function $f (x) =$ $| x^{2} - 7 x + 10 |$ $- 5 x + 27, x \in [- 2, 14]$ then $m + n$ is

Ans.
(2)

$y =$ ${\begin{matrix} x^{2} - 12 x + 37, & x \leq 2 \\ 2 x - x^{2} + 17, & 2 < x < 5 \\ x^{2} - 12 x + 37, & x \geq 5 \end{matrix}}$

$y = a x^{2} + b x + c$